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b^2+(b +1)^2+...+(b + a)^2 -3 mutiple of 5, a+b = odd, digit of units of (a+b)?

Source: Rioplatense Olympiad 2000 level 3 P1

September 6, 2018

number theoryoddmultipleLast digit

Problem Statement

Let

a

and

b

be positive integers such that the number

b^2 + (b +1)^2 +...+ (b + a)^2-3

is multiple of

5

and

a + b

is odd. Calculate the digit of the units of the number

a + b

written in decimal notation.