# Eqaution with 2 variables

• Dec 20th 2009, 07:19 AM
Stylis10
Eqaution with 2 variables
Prove that there do not exist integers $m,n \in \mathbb{Z}$ such that $14m + 20n = 119$

Im not quite sure how to go about proving this
• Dec 20th 2009, 07:32 AM
HallsofIvy
Quote:

Originally Posted by Stylis10
Prove that there do not exist integers $m,n \in \mathbb{Z}$ such that $14m + 20n = 119$

Im not quite sure how to go about proving this

Notice that the two coefficients, 14 and 20, are both even. That is, they are divisible by 2 and, no matter what m and n are, 14m+ 20n= 2(7m+10n) is divisible by 2.
• Dec 20th 2009, 07:40 AM
Stylis10
Quote:

Originally Posted by HallsofIvy
Notice that the two coefficients, 14 and 20, are both even. That is, they are divisible by 2 and, no matter what m and n are, 14m+ 20n= 2(7m+10n) is divisible by 2.

I realised that, but surely that cant be the whole proof, i just dont know how to give more that what you have said, that answer alone cant be worth 4 marks