Find the integer n, 0 n 6, such that n 100000 7.

Since 100000 5 7, the integer n we seek is n = 5.

jmc

number theory intermediate

Problem

Find the integer

n

0 \leq n \leq 6

, such that

n \equiv 100000 (mod 7) .

Solution

Since

100000 \equiv 5 (mod 7)

, the integer

n

we seek is

n = 5

Final answer