Warm up problem: integer solutions easy

Number Theory Level 2

Find the number of all integer triples (a,b,c) such that a ( a + 2 b + 2 c ) + b ( b + 2 c ) + c 2 = 2 a(a+2b+2c)+b(b+2c)+c^2=2

1 5 2 0

Trevor Arashiro by Trevor Arashiro , 22, USA

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1 solution

Kelly Bumr
Sep 18, 2014

Rearranging : ( a + b + c ) 2 = 2 (a+b+c)^2=2 , which means a + b + c = 2 a+b+c= \sqrt{2} . There's no triplet of integers that qualify that.

[LaTeX edits: moderator]

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