Greatest Integer and Remainder | TOMATO B.Stat Objective 113
Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Greatest Integer and remainder.
Greatest integer and remainders (B.Stat Objective Question)
The greatest integer which, when dividing the integers 13511, 13903 and 14593 leaves the same remainder is
Key Concepts
Check the Answer
Answer: 2.
B.Stat Objective Problem 113
Challenges and Thrills of Pre-College Mathematics by University Press
Try with Hints
here all numbers are odd
13511, 13903 and 14593 leaves different remainders when divided by 98, 56 and 7
13511, 13903 and 14593 leaves same remainder when divided by 2
then greatest integer 2.
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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
f(94)=\(94^{2}-f(93)=94^{2}-93^{2}+f(92)\)
=\(94^{2}-93^{2}+92^{2}-f(91)\)
=\((94^{2}-93^{2})+(92^{2}-91^{2})\)
\(+....+(22^{2}-21^{2})+20^{2}-f(19)\)
=94+93+.....+21+400-94
=4561
\(\Rightarrow\) remainder =561.
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