×

# Proving for primes

For a given prime $$p > 2$$ and positive integer $$k$$ let $S_k = 1^k + 2^k + \ldots + (p - 1)^k$

Find those values of $$k$$ for which $$p \, |\, S_k$$.

Note by Lakshya Sinha
1 year, 11 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

all values of $$k$$ such that $$p-1$$ does not divide $$k$$.

- 1 year, 10 months ago

Some solutions are k=1,2,3,p

- 1 year, 11 months ago

k should not be the multiple of $$\phi (p)$$ will always satisfy.

- 1 year, 11 months ago