MATHS OLYMPIAD [stage1] 2018 (INDIA)
Integers , , and satisfy
What is the sum of all possible values of ?
The answer is 18.
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1 solution
a + b – c = 1, a^2 + b^2– c^2 = – 1 a + b – 1= c
a^2 + b^2 + 1 + 2ab – 2(a + b) = c^2
(a – 1) (b – 1) = 1
So a – 1 = b – 1 = ±1
a = b = 2 or a = b = 0
So c = 3 (when a = b = 2) or c = –1 (when a = b = 0)
Hence a^2 + b^2 + c^2 = 17 or 1
Sum = 18