# Difference between revisions of "2021 JMPSC Sprint Problems/Problem 20"

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<math>257^3 = 16974593</math>, <math>256^2 = 65536</math>, and <math>257^2 = 66049</math>. | <math>257^3 = 16974593</math>, <math>256^2 = 65536</math>, and <math>257^2 = 66049</math>. | ||

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+ | ==See also== | ||

+ | #[[2021 JMPSC Sprint Problems|Other 2021 JMPSC Sprint Problems]] | ||

+ | #[[2021 JMPSC Sprint Answer Key|2021 JMPSC Sprint Answer Key]] | ||

+ | #[[JMPSC Problems and Solutions|All JMPSC Problems and Solutions]] | ||

+ | {{JMPSC Notice}} |

## Revision as of 17:14, 11 July 2021

## Contents

## Problem

For all integers and , define the operation as Find

## Solution

Let . Then, and . We substitute these values into expression to get Recall the definition for the operation ; using this, we simplify our expression to We have and , so we can expand the numerator of the fraction within the square root as to get ~samrocksnature

## Solution 2

Basically the same as above, but instead we can let . Then we have

which equals .

~~abhinavg0627

## Note:

, , and .

## See also

The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition.