[HS Math] Mathematical Induction help.

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morroblivion is in HS math

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Last time I encountered it wad 2nd year hs, but now I'm seeing it again for my after school math activities. I'm stuck at one item.

Prove that 5^{2n 1} x 2^{n 2} 3^{n 2} x 2^{2n 1} is divisible by 19.

How I remember doing it in 2nd year is adding like an extra term to the given, but now they in the handout I have it doesnt say so.

I googled a bit and tried to get a polynomial with the exponents as k and this poly (assumption so far I think?) is divisible by 19. Whenever I do k 1 however I can't prove that the poly is divisible by 19. Any idea on what I should do?

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