Find a formula for the integer with smallest absolute value that is congruent to an integer a modulo m. where m is a positive integer.

Solution: Step 1 :In this problem we have to find a formula for the the integer with smallest absolute value. In this problem given that the smallest absolute value that is congruent to an integera modulo m.Consider an integer x, from the definition Where k is an integer From the division algorithm Where q is quotient.