Problem:
Let
x=(5+1)(45+1)(85+1)(165+1)4
Find (x+1)48.
Solution:
Let y=165. Then
x=(y8+1)(y4+1)(y2+1)(y+1)4=(y8+1)(y4+1)(y2+1)(y+1)(y−1)4(y−1)=y16−14(y−1)=5−14(y−1)=y−1
Thus (x+1)48=y48=53=125.
The problems on this page are the property of the MAA's American Mathematics Competitions