I am trying to work out if 4a^3+5a is always a multiple of 3 for positive integers.
I have thought about splitting a into odd and even numbers:
So if a is even (say 2k) we get 4(2k)^3 + 5(2k) = 32k^3 +10k = k(32k^2 +10) but this doesn't appear to go anywhere?
I have also thought about rewriting 4a^3+5a as perhaps 4a^3+ 4a + a = 4a(a^2+1) + a
so if a = even, a^2 is even etc.. but i can't conclude from that it is a multiple of 3.
Then i am thinking maybe it is not always a multiple of 3 ??
Any hints?
I have thought about splitting a into odd and even numbers:
So if a is even (say 2k) we get 4(2k)^3 + 5(2k) = 32k^3 +10k = k(32k^2 +10) but this doesn't appear to go anywhere?
I have also thought about rewriting 4a^3+5a as perhaps 4a^3+ 4a + a = 4a(a^2+1) + a
so if a = even, a^2 is even etc.. but i can't conclude from that it is a multiple of 3.
Then i am thinking maybe it is not always a multiple of 3 ??
Any hints?