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# Modular arithmetic watch

1. 1) Show 5^14 = 10 (mod 15).

In the question it says it may be useful to find 5^14 mod 3 and mod 5, so I've done that:

By FLT, 5^2 = 1 (mod 3), so 5^14 = 1 (mod 3), so 5^14 - 10 = 0 (mod 3)

5^14 = 0 (mod 5), so 5^14 - 10 = 0 (mod 5)

Unsure about where to go from here, been stuck for ages, pls help

Zacken
2. (Original post by Gome44)
...
You've just proven that is a multiple of both and , and ...
3. (Original post by Zacken)
You've just proven that is a multiple of both and , and tex]3 \times 5 = 15[/tex]...
lol im stupid
4. (Original post by Gome44)
lol im stupid

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