Problem Solving

1 . what is the remainder when 128^500 is divided by 153?

I understood till

Euler number of 153 is 96 so the number reduces to 128^20

153 = 17 * 9

Now he says..
17 leaves a remainder of 16 and 9 leaves a remainder of 4
17A+16= 9B + 4

How exactly did he come to that conclusion ??



2.(36^41) mod 7 = 1 ?? how
(36^41) mod 11 = 3 ?? how again

i understand mod is %.. but am unable to work it out

please help !

Anyone !!??

Ajax12 wrote:1 . what is the remainder when 128^500 is divided by 153?

I understood till

Euler number of 153 is 96 so the number reduces to 128^20

153 = 17 * 9

Now he says..
17 leaves a remainder of 16 and 9 leaves a remainder of 4
17A+16= 9B + 4

How exactly did he come to that conclusion ??



2.(36^41) mod 7 = 1 ?? how
(36^41) mod 11 = 3 ?? how again

i understand mod is %.. but am unable to work it out

please help !

The theorems that are supportive in solving such kind of problems are:

1. Euler's Theorem
2. Fermat's Little Theorem
3. Wilson's Theorem
4. Chinese Remainder

All of these theorems are out of scope for GMAT. Even then if the curiosity is there; please post it in GMAT Math sub forum to know more about that. Serious GMAT aspirants may please ignore this thread. This page will be useful: https://www.math-help-ace.com/Elementary ... heory.html