Difference between revisions of "2005 Canadian MO Problems/Problem 2"
m (fmt) |
m (→See also) |
||
Line 19: | Line 19: | ||
==See also== | ==See also== | ||
− | |||
− | |||
*[[2005 Canadian MO]] | *[[2005 Canadian MO]] | ||
+ | {{CanadaMO box|year=2005|num-b=1|num-a=3}} | ||
[[Category:Olympiad Algebra Problems]] | [[Category:Olympiad Algebra Problems]] | ||
[[Category:Olympiad Number Theory Problems]] | [[Category:Olympiad Number Theory Problems]] |
Revision as of 18:46, 7 February 2007
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
.
Solution
We have
By AM-GM, we have
where is a positive real number not equal to one. If
, then
. Thus
and
. Therefore,
See also
2005 Canadian MO (Problems) | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 | Followed by Problem 3 |