simple one

if x and y are positive integers such that the last digit of x²+xy+y² is 0 , then prove that last 2 digits of x²+xy+y² are 0

2 Answers

this is kind of simple

first take 2 divides x .. then 2 should divide y

similaryly take 5 divides x then 5 should divide y

hence the proof :)

good method. even congruencies would work. use fact that a square should end with 0,1,4,5,6,9

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