Number Theory - Fermat's Little Theorem & Halley's Comet

[Jamers328]

Here is the problem:

The three most recent appearances of Halley's comet were in the years 1835, 1910, and 1986; the next occurrence will be in 2061. Prove that

1835^1910 + 1986^2061 = 0 (mod 7)

I don't necessarily have to write out a whole proof, but I do have to explain how this is true, and I can use FlT (Fermat's little thm).

 

[daon]

Well, using Fermat's Thm, \(\displaystyle 1835^6=1 \,\, (mod \,\, 7)\) and \(\displaystyle 1986^6=1 \,\, (mod \,\, 7)\).

 

[Jamers328]

Thanks... I figured it out.