1995 Remainder

When an integer is divided by 1995, the remainder is 75. When the same integer is divided by 57, what will be the remainder?
Source: mathcontest.olemiss.edu 2/6/2012

Let n be the integer. By definition of division remainder, there exists a quotient q such that
n=q\left (1995\right )+75
=q\left (35\times 57\right )+\left (57+18\right )
Factor 57
n=57\left (35q+1\right )+18
Let p=35q+1
n=p\left (57\right )+18
The remainder equals 18 when the same integer n is divided by 57.

Answer: 18.


About mvtrinh

Retired high school math teacher.
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