Help me!!!

For how many positive integers k, does there exists a non-constant function fk from the reals to the reals, which is periodic with fundamental period k, and for all real values of x satisfies the equation fk(x−30)+fk(x+600)=0?

Details and assumptions

The fundamental period of a non-constant function f on the reals is the smallest non-negative value α such that f(x)=f(x+α) for all real x.

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
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Comments

Kindly stop posting live problems here.

Vikram Waradpande - 7 years, 8 months ago

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Calvin Lin Staff - 7 years, 8 months ago

Math	Appears 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}`	$\boxed{123}$