Difference between revisions of "2013 USAJMO Problems/Problem 1"

Revision as of 20:30, 11 May 2013

Are there integers $a$ and $b$ such that $a^5b+3$ and $ab^5+3$ are both perfect cubes of integers?

Consider the equation modulo $9$ .

Revision as of 20:30, 11 May 2013 (view source) Countingkg (talk \| contribs) ← Older edit		Revision as of 20:30, 11 May 2013 (view source) Countingkg (talk \| contribs) Newer edit →
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	==Solution==		==Solution==

−	Consider the equation <math>~~\bmod~~ 9</math>.	+	Consider the equation modulo <math>9</math>.