Number Theory

[limpid abyss]

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[rough rain]

I know that I have to use congruency and that 119 is not prime because it is 17*7

I think I need to use Fermat's little problem but Idk how to apply it when the number divided by isn't prime, do I need to make the congruency for 17 and 7? Also I don't see how to make the exponents be the p-1 to apply the Fermat's theorem

[analog zinc]

@rough rain Your question most likely won't be answered properly. I suggest you to find the math olympiad server. They are great at number theory.

[rough rain]

are you fr?

[analog zinc]

Yes

I'm being honest

I can provide you with an invite

[rough rain]

I mean I'm in my 1st year of university so the problem shouldn't be very hard

[rough rain]

sure send me please

[analog zinc]

DMs

I sent it

[rough rain]

thanks

[sand cove]

$\gcd(5,119)=1$, so $5^{\varphi(119)}\equiv 1\mod 119$

[potent flame]

Omegabet_

[sand cove]

$\varphi(119)=\varphi(7\times 17)=119(1-\frac{1}{7})(1-\frac{1}{17})$

[potent flame]

Omegabet_

[sand cove]

rest is then just reducing 960101 by phi(119)

[sand cove]

FlT generalizes to reduction mod n in the following manner: If $\gcd(a,n)=1$, then $a^{\varphi(n)}\equiv 1\mod n$

[potent flame]

Omegabet_

[rough rain]

understood thanks, I had forgotten that I could also use Euler's

[thin jungle]

@rough rain has given 1 rep to @sand cove

[sand cove]

might have to do it a couple times, but should eventually spit out the answer

[rough rain]

euler of 119 is 96 so I'll be able to apply it on 5^960101. I'll try to solve it

[sand cove]

yep, so you want to reduce 960101 mod 96

[rough rain]

I got the right answer: 118. Thanks again Omega