# 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>. | ||

+ | |||

+ | == Solution 3 == | ||

+ | Notice that <math>x=y+1</math>, substituting this in, we get <math>x^2(x+1)</math>. Therefore, <math>\sqrt{\frac{257^2(258)}{258}}=\boxed{257}</math> | ||

==See also== | ==See also== |

## Revision as of 09:59, 12 July 2021

## 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 .

## Solution 3

Notice that , substituting this in, we get . Therefore,

## See also

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