Prove that there do not exist integers $\displaystyle m,n \in \mathbb{Z} $ such that $\displaystyle 14m + 20n = 119$
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.
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