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May 3, 2020

Remainders and Functions | AIME I, 1994 | Question 7

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1994 based on Remainders and Functions.

Remainders and Functions - AIME I, 1994

The function f has the property that, for each real number x, \(f(x)+f(x-1)=x^{2}\) if f(19)=94, find the remainder when f(94) is divided by 1000.

  • is 107
  • is 561
  • is 840
  • cannot be determined from the given information

Key Concepts




Check the Answer

Answer: is 561.

AIME I, 1994, Question 7

Elementary Number Theory by David Burton

Try with Hints

First hint



Second Hint



Final Step



\(\Rightarrow\) remainder =561.

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