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 16:14, 11 July 2021
Contents
[hide]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.