2024 AMC 10A Problems/Problem 15
Revision as of 16:03, 8 November 2024 by MRENTHUSIASM (talk | contribs)
Problem
Let be the greatest integer such that both
and
are perfect squares. What is the units digit of
?
Solution
Let and
for some positive integers
and
We subtract the first equation from the second, then apply the difference of squares:
Note that
and
have the same parity, and
We wish to maximize both and
so we maximize
and minimize
It follows that
from which
~MRENTHUSIASM
See also
2024 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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