and <math>p^2 + 3</math> have no common factors (since they differ impossible (because two squares differ by more than <math>2</math>). ...

...o choose from). However, we must subtract the ways where two white squares differ by a rotation of 90 degrees about the middle of the square. There are a tot ...ion of 90 degrees and minus when there are 3 squares such that two of them differ by rotation of 90 and 1 of them differs by rotation of 180, because of the ...

...th> shapes (circle, hexagon, square, triangle). How many blocks in the set differ from the 'plastic medium red circle' in exactly <math>2</math> ways? (The ' ...he 'plastic medium red circle' in one of its qualities <math>(1)</math> or differ from it in <math>k</math> different ways <math>(kx)</math>. Choosing the ma ...

...g of six digits (from 0 through 9). The state requires that any two plates differ in at least two places. (Thus the plates <math>\boxed{027592}</math> and <m ...plates which agree on the first <math>n-1</math> digits; these plates thus differ only on one digit, the last one. ...

...larly, if they differ by 3, there will be only 1 possible set, and if they differ by 1, 3 possible sets. ...so the condition is met. Now, this means that the multiple of 6 and 7 must differ by 1. ...

...differ by <math>20</math> and another pair of complementary divisors that differ by <math>23</math>. What is the sum of the digits of <math>N</math>? Since we are given that some pairs of divisors differ by 20 and 23 and we can let the pair be <math>(x-10)</math> and <math>(x+10 ...

...keeping track of different license places easier, each license plate much differ from every other license plate by at least <math>2</math> digits. For examp ...plates which agree on the first <math>n-1</math> digits; these plates thus differ only on one digit, the last one. ...

...first two, and <math>7</math> choices for the fourth number, since it must differ from all three. This means there are <math>9 \times 9 \times 8 \times 7=\b ...

...this process continues until the last two numbers that remain on the board differ by at least 2. Let <math>f(k)</math> be the smallest positive integer not w ...ill show the hundreds place at the end. In order for the hundreds place to differ by 2, the difference between two perfect squares needs to be at least <math ...

...e <math>P</math> is the probability that <math>B</math> and <math>J</math> differ by <math>1</math> (no zero, because the two numbers are distinct). There ar ...h>, the numbers differ by less than 2, so the probability that the numbers differ by at least 2 is <math>1-\tfrac{19}{190}=\tfrac9{10}</math>. Then <math>B-J ...

If two numbers differ by <math>2</math> and their sum is <math>20</math>, the larger number is Let <math>x</math> be the larger number. Since the numbers differ by <math>2</math>, the smaller number must be <math>x - 2</math>. Thus, we ...

If two numbers differ by <math>2</math> and their sum is <math>20</math>, the larger number is Let <math>x</math> be the larger number. Since the numbers differ by <math>2</math>, the smaller number must be <math>x - 2</math>. Thus, we ...

...ree terms form a [[geometric progression]], and the first and fourth terms differ by <math>30</math>. Find the sum of the four terms. Since the first and fourth terms differ by <math>30</math>, we have that <math>\frac{(a + 2d)^2}{a + d} - a = 30</m ...

...eorem. The converse follows because <math>a</math> and <math>b</math> must differ by a multiple of <math>m</math> and <math>n</math>, and <math>\mbox{lcm}(m, ...r]]. Moreover, in the case when the problem is solvable, any two solutions differ by some [[common multiple]] of <math>m_1,\ldots,m_n</math>.'' (the extended ...

We know that 1 and 5 differ by 4, 5 and 13 differ by 8, and 13 and 25 differ by 12. Hence the differences are 4, 8, and 12, resp. And the differences of ...

...math>). All additional triangles will differ by one as the solutions above differ by one so this process can be repeated indefinitely until the side lengths ...

...ots \; , 20 \}</math> of size <math>n</math> must contain two numbers that differ by 8? ...; \{ 12, 20 \}</math> in <math>\{ 1, 2, 3, \; \dots \; , 20 \}</math> that differ by 8. If we take <math>n = 12</math>, it could be that we selected one elem ...

...square roots of the numbers which are also the product of numbers which '''differ by 2.''' It is found that the square root of the product may differ to maximum of 0.3 from actual middle number, but this is negligible unless ...

...one but shh for the sake of clarity). <math>99</math> and <math>71</math> differ by <math>28</math>, so a difference of merely <math>8</math> in <math>a</ma ...

...differ by <math>20</math> and another pair of complementary divisors that differ by <math>23</math>. What is the sum of the digits of <math>N</math>? ...