1982 AMC 12 Problem 26
Attempt Problem 26 of the 1982 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1982 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
26.
If the base representation of a perfect square is where then is
not uniquely determined
Answer: B
Small hint:
Only the last two base- digits matter modulo
Big hint:
List the quadratic residues modulo that lie between and
Solution:
The last two octal digits represent Squares modulo in the range include only Thus so
Therefore, the correct answer is B.
Problem 26 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
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