number theory

[dark latch]

32 = 7 * 4 + 4

By Fermat's little theorem
k^7 = k for all k,

So (k^7)^4 = k^4 [mod 7]
And then k^(4 * 7) * k^4 = k^8 mod 7

So k^32 = k^8 mod 7

Again, applying the theorem gives :
k^7 = k mod 7
Implies k^8 = k^2 mod 7

The sum of k^2 from k=1 to k = 100 is 338350
Which you can easily find the remainder when divided by 7

[sweet steeple]

how do you know all of that stuff

bro is some genius or sum

[dark latch]

Far from it unfortunately

😁

[sweet steeple]

respect though still

you got some grips

you studying maths?

[dark latch]

Used to

[paper marsh]

338350≡5 (mod7) so 5 is the correct answer

[dark latch]

Yup

,w (sum k^32 from k = 1 to k= 100) mod 7