Difference between revisions of "2022 SSMO Relay Round 2 Problems/Problem 3"
(Created page with "==Problem== Let <math>T =</math> TNYWR. Let <math>a+b = \lfloor \sqrt{T} \rfloor</math>. If <math>a^5 + b^5 = 15</math>, then <math>ab</math> has two possible values. The abso...") |
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==Problem== | ==Problem== | ||
| − | Let <math>T =</math> | + | Let <math>T =TNYWR</math>. Let <math>a+b = \lfloor \sqrt{T} \rfloor</math>. If <math>a^5 + b^5 = 15</math>, then <math>ab</math> has two possible values. The absolute difference of these values is <math>\frac{x\sqrt{y}}{z}</math>, where <math>x,y</math> and <math>z</math> are positive integers, <math>x</math> and <math>z</math> are relatively prime, and <math>y</math> is not divisible by the square of any prime. What is <math>x+y+z?</math> |
==Solution== | ==Solution== | ||
Latest revision as of 19:23, 2 May 2025
Problem
Let 
. Let 
. If 
, then 
has two possible values. The absolute difference of these values is 
, where 
and 
are positive integers, 
and are relatively prime, and 
is not divisible by the square of any prime. What is 
