Clarification....

I am trying to answer this problem: https://brilliant.org/community-problem/primeprimeprime/?group=0jEjslvgEVDa

The answer should be 5. I think because p^2 is congruent to 1 modulo 4 (for p >= 3). From the equation: p^2 - 2q^2 = 1 and so... p^2 - 1 = 2q^2 .... 2q^2 is divisible by 4 and so q^2 is even and sqrt of q^2 must be even but no prime except 2 satisfies this...

P.S. Do you have any advice on how to solve level 4 or 5 problems?.... I sometimes (in despair) use trial and error method....

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Comments

Thanks, I've updated the answer accordingly. Can you add a solution to it?

Calvin Lin Staff - 7 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$