Date: Thu, 17 Apr 1997 11:44:48 -0400

From: Alexander Bogomolny

Yes, of course.

You are looking for a number k such that 81k+65 is divisible by 8. The simplest way is to use the modulo arithmetic:

81 = 1 (mod 8) and 65 = 1 (mod 8)

which only means that the remainder of division by 8 is 1 in both cases. Your equation is equivalent to

1*k + 1 = 0 (mod 8)

Or

k = -1 (mod 8)

Note that -1 = 7 (mod 8) which gives your result.

Modulo arithmetic is exactly the same except at every stage you substitute the remainder.

Best regards,

Alexander Bogomolny