Show that { (m, n): 17 divides 2m + 3n} = { (m, n): 17 divides 9m + 5n}.
Solution
Put N = 2m+3n, M = 9m+5n. 17|N implies 17|(13N-17(m+2n)) = M. Similarly, 17|M implies 17|(4M-17(2m+n)) = N.
© John Scholes
jscholes@kalva.demon.co.uk
8 Oct 2003
Last corrected/updated 8 Oct 03