15 January 2020

• 11:4611:46, 15 January 2020 diff hist +916 2006 iTest Problems/Problem 19 →Solution
• 11:4311:43, 15 January 2020 diff hist −2 2006 SMT/General Problems/Problem 16 →Solution current
• 11:4311:43, 15 January 2020 diff hist +71 2006 SMT/General Problems/Problem 16 →Solution
• 11:3711:37, 15 January 2020 diff hist +2 m 2006 SMT/Calculus Problems/Problem 2 →Solution current

14 January 2020

• 17:3917:39, 14 January 2020 diff hist +96 2006 SMT/Team Problems/Problem 8 →Solution current
• 17:3817:38, 14 January 2020 diff hist +275 m 2006 SMT/Team Problems/Problem 13 →Solution current
• 17:3717:37, 14 January 2020 diff hist +282 m 2006 SMT/Team Problems/Problem 15 →Solution current
• 17:3717:37, 14 January 2020 diff hist 0 m 2006 SMT/General Problems/Problem 8 →Solution current
• 17:3617:36, 14 January 2020 diff hist +12 m 2006 SMT/General Problems/Problem 8 →Solution
• 17:3617:36, 14 January 2020 diff hist +104 m 2006 SMT/General Problems/Problem 10 →Solution current
• 17:3517:35, 14 January 2020 diff hist −2 m 2006 SMT/General Problems/Problem 8 →Problem 8
• 17:3517:35, 14 January 2020 diff hist +311 m 2006 SMT/General Problems/Problem 16 →Solution
• 17:3417:34, 14 January 2020 diff hist +269 m 2006 SMT/General Problems/Problem 13 →Solution current
• 17:3317:33, 14 January 2020 diff hist +325 2006 SMT/General Problems/Problem 8 →Solution
• 17:3217:32, 14 January 2020 diff hist +91 m 2006 SMT/Calculus Problems/Problem 6 →Solution current
• 17:3117:31, 14 January 2020 diff hist +60 m 2006 SMT/Calculus Problems/Problem 5 →Solution current
• 17:3117:31, 14 January 2020 diff hist +158 m 2006 SMT/Calculus Problems/Problem 2 →Solution
• 17:3017:30, 14 January 2020 diff hist −59 m 2006 SMT/Advanced Topics Problems/Problem 10 →Problem 10 current
• 17:3017:30, 14 January 2020 diff hist +157 m 2006 SMT/Advanced Topics Problems/Problem 10 →Solution
• 17:2717:27, 14 January 2020 diff hist +532 2006 iTest Problems/Problem 37 →Solution current
• 17:2717:27, 14 January 2020 diff hist +532 2006 iTest Problems/Problem 20 →Solution
• 17:2617:26, 14 January 2020 diff hist +532 2006 iTest Problems/Problem 19 →Solution
• 17:1917:19, 14 January 2020 diff hist +565 N 2006 SMT/General Problems/Problem 16 Created page with "==Solution== The condition we are looking for is <math>35(n-1)\equiv 0 \mod 360</math>, because if any other <math>A_n = A_1</math> than <math>35(n-1)</math> must be a multip..."
• 17:0617:06, 14 January 2020 diff hist +14 m 2006 SMT/General Problems/Problem 12 No edit summary current
• 17:0117:01, 14 January 2020 diff hist +316 N 2006 SMT/General Problems/Problem 12 Created page with "Noticing that the sum of the digits of 8091 is 18, we can divide 8091 by 9, yielding 899. Testing all prime numbers up to <math>\sqrt{899} \approx 30</math>, we see that 899 i..."
• 16:5316:53, 14 January 2020 diff hist +977 N 2006 SMT/Advanced Topics Problems/Problem 10 Created page with "==Solution== First of all, remember that <cmath>\arctan(a)+\arctan(b) = \arctan(\frac{a+b}{1-ab}) +k\pi </cmath> Therefore we want <math>a</math> and <math>b</math> such tha..."
• 16:1516:15, 14 January 2020 diff hist +610 N 2006 SMT/Calculus Problems/Problem 5 Created page with "==Solution== Using integration by parts, we find that the desired integral is equal to: <cmath>\begin{align*} \int(x\tan^{-1}x)dx &= \frac{x^2}{2}\tan^{-1}x-\int\frac{x^2}{2..."
• 15:5615:56, 14 January 2020 diff hist +699 N 2006 SMT/Calculus Problems/Problem 2 Created page with "==Solution== Substituting <math>y=e^{\lambda t}</math> into the differential equation, we can solve for the values of <math>\lambda</math>: <cmath>\begin{align*} 0&=4y''+3y'..."
• 14:3114:31, 14 January 2020 diff hist +1,032 N 2006 SMT/Calculus Problems/Problem 6 Created page with "==Solution== Let <math>u=\frac{\pi}{2}-x</math> and <math>du=-dx</math>, the integral than turns into: <cmath> I = \int_{0}^{\pi/2}\frac{\sin^3x}{\sin^3x+\cos^3x}dx \Rightar..."
• 14:0914:09, 14 January 2020 diff hist +2,190 N 2006 iTest Problems/Problem 20 Created page with "==Solution== <asy> unitsize(2.5); draw((0,0)--(0,90)--(90,90)--(90,0)--cycle,linewidth(2)); draw((10,0)--(10,90)); draw((20,0)--(20,90)); draw((30,0)--(30,90),linewidth(2));..."
• 13:5613:56, 14 January 2020 diff hist +2,181 N 2006 iTest Problems/Problem 19 Created page with "==Solution== <asy> unitsize(2.5); draw((0,0)--(0,90)--(90,90)--(90,0)--cycle,linewidth(2)); draw((10,0)--(10,90)); draw((20,0)--(20,90)); draw((30,0)--(30,90),linewidth(2));..."
• 13:1213:12, 14 January 2020 diff hist +625 N 2006 SMT/Team Problems/Problem 6 Created page with "==Solution== Rewriting <math> 16^n+4^n+1 </math> as <math>2^{4n}+2^{2n}+1</math> we can set the two given expressions equal to each other. <cmath>\begin{align*} \frac{(2^{p(..." current
• 12:5912:59, 14 January 2020 diff hist +1,084 N 2006 SMT/Team Problems/Problem 8 Created page with "==Solution== To begin, let's rewrite the sum as <cmath>\lim_{n\to\infty} \sum_{k=n^2}^{(n+1)^2} \frac{1}{\sqrt{k}} = \lim_{n\to\infty} \sum_{k=0}^{2n+1} \frac{1}{\sqrt{n^2+..."
• 12:4312:43, 14 January 2020 diff hist +1,220 N 2006 SMT/Team Problems/Problem 13 Created page with "==Solution== A line that passes through the origin has an equation of <math>y=mx</math>. If the line <math>y=mx</math> is tangent to the hyperbola than the equation <math>(mx..."
• 12:2612:26, 14 January 2020 diff hist +2,599 N 2006 SMT/Team Problems/Problem 15 Created page with "==Solution== Denote <math>\prod_{i=0}^{\infty} \frac{c_i^{2}}{c_i^{2}-1}</math> as <math>\prod_{composite} \frac{c^2}{c^2-1}</math>. To begin, let <math>S</math> = <math>\pro..."

13 January 2020

• 17:3617:36, 13 January 2020 diff hist +544 N 2006 SMT/General Problems/Problem 14 Created page with "==Solution== Noticing that the first equation, <math>x^2+y^2\le\pi^2</math> is the equation of a disk of radius <math>\pi</math>, and that the graph of <math>y = sin(x)</math..." current
• 17:2017:20, 13 January 2020 diff hist +245 N 2006 SMT/General Problems/Problem 13 Created page with "==Solution== This solution does require quite a bit of guessing and testing, but if we notice that we want the numbers to be relatively close so that no term "dominates" the..."
• 17:1017:10, 13 January 2020 diff hist +9 m 2006 SMT/General Problems/Problem 10 →Solution
• 17:1017:10, 13 January 2020 diff hist +9 m 2006 SMT/General Problems/Problem 10 →Solution
• 17:0917:09, 13 January 2020 diff hist +58 2006 SMT/General Problems/Problem 10 →Solution
• 17:0617:06, 13 January 2020 diff hist +2 m 2006 SMT/General Problems/Problem 10 →Solution
• 17:0617:06, 13 January 2020 diff hist +15 2006 SMT/General Problems/Problem 10 →Solution
• 17:0617:06, 13 January 2020 diff hist +316 2006 SMT/General Problems/Problem 10 →Solution
• 16:5916:59, 13 January 2020 diff hist −567 2006 SMT/General Problems/Problem 10 →Solution Tag: Replaced
• 16:5816:58, 13 January 2020 diff hist +579 N 2006 SMT/General Problems/Problem 10 Created page with "==Solution== First of all, lets note that the sum of all positive integers from <math>1</math> to <math>n</math> inclusive is <math>\frac{n(n+1)}{2}</math>. The sum of all nu..."
• 16:4216:42, 13 January 2020 diff hist +1,227 N 2006 SMT/General Problems/Problem 8 Created page with "==Solution== Assuming all the numbers are positive, lets denote the five numbers as <math>a_0,a_1,a_2,a_3,a_4</math>. Assume WLOG that <math>a_0 \ge a_1 \ge a_2 \ge a_3 \ge a..."
• 15:5515:55, 13 January 2020 diff hist +754 N 2013 PMWC Problems/Problem I15 Created page with "==Solution== First of all, note that <math>M=\sum_{n=1}^\infty \frac{1}{k^2}</math>, and that <math>K=\sum_{n=1}^\infty \frac{1}{(2k-1)^2}</math> Splitting <math>M</math> in..." current
• 15:0215:02, 13 January 2020 diff hist +2,801 N 2006 iTest Problems/Problem 37 Created page with "==Solution== To begin, let's number the equations as follows <cmath>\begin{align} x^2 + xy + y^2 &= 1 \\ y^2 + yz +z^2 &= 2 \\ z^2 + zx +x^2 &= 3 \end{align}</cmath> In or..."
• 15:0215:02, 13 January 2020 diff hist −2,802 2006 iTest Problems →Solution
• 15:0115:01, 13 January 2020 diff hist +2,803 2006 iTest Problems →Problem 37