?

Number Theory Level 3

p p and q q are prime numbers so that:

p 3 − q 5 = ( p + q ) 2 {p}^{3}-{q}^{5}={(p + q)}^{2} .

Find p + q p + q .


The answer is 10.

Adrian Neacșu by Adrian Neacșu , 33, Romania

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2 solutions

Finn Hulse
Apr 26, 2014

I seriously got it my first time. I plugged in p = 7 p=7 and q = 3 q=3 . In fact... wait a second. I posted this problem here . Great minds think alike! I came up with it in the back of math class. :O

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Ramiel To-ong
Dec 8, 2015

nice problem

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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