Problem: If r is the remainder when each of the numbers 1059,1417 and 2312 is divided by d, where d is an integer greater than one, then d−r equals
Answer Choices:
A. 1
B. 15
C. 179
D. d−15
E. d−1
Solution:
Since d divides 2312−1417=(5)179 and 1417−1059=(2)179 (and 179 is prime ), d=179,r=164 and d−r=15.