2005 Canadian MO Problems/Problem 2: Difference between revisions
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==Problem== | ==Problem== | ||
Let <math>(a,b,c)</math> be a Pythagorean triple, ''i.e.'', a triplet of positive integers with <math>a^2+b^2=c^2</math>. | Let <math>(a,b,c)</math> be a Pythagorean triple, ''i.e.'', a triplet of positive integers with <math>{a}^2+{b}^2={c}^2</math>. | ||
* Prove that <math>(c/a + c/b)^2 > 8</math>. | * Prove that <math>(c/a + c/b)^2 > 8</math>. | ||
Revision as of 17:52, 28 July 2006
Problem
Let 
be a Pythagorean triple, i.e., a triplet of positive integers with 
.
- Prove that
. - Prove that there does not exist any integer
for which we can find a Pythagorean triple 
satisfying 
.
.
for which we can find a Pythagorean triple 
.
