Difference between revisions of "2007 JBMO Problems/Problem 4"
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Latest revision as of 14:33, 16 April 2024
Problem 4
Prove that if is a prime number, then is not a perfect square.
Solution
By Fermat's Little Theorem, . By quadratic residues, this is true if and only if , except for (which doesn't work). Then, , but this implies is odd, so cannot be a perfect square.
See also
2007 JBMO (Problems • Resources) | ||
Preceded by Problem 3 |
Followed by Last Problem | |
1 • 2 • 3 • 4 | ||
All JBMO Problems and Solutions |