Divisibility #3

Number Theory Level 3

It is know that ( a + b ) (a+b) definitely divides ( a 2 m + 1 + b 2 m + 1 ) ({ a }^{ 2m+1 }+{ b }^{ 2m+1 }) as long as a , b , m a,b,m are whole numbers.

For how many tuples ( a , b , m ) (a,b,m) does ( a + b ) (a+b) divide ( a 2 m + b 2 m ) ({ a }^{ 2m }+{ b }^{ 2m }) where a , b , m a,b,m are distinct positive integers greater than 100?

Please notify any mistakes.

Infinte 0 243 81

Maninder Dhanauta by Maninder Dhanauta , 22, Canada

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Siva Budaraju
Nov 6, 2017

Just set a a and b b to 1, and m m to any arbitrary number.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

@Siva Budaraju I fixed my solution to exclude this case. Clever thinking though.

Maninder Dhanauta - 3 years, 7 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...