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28 Dec 2021, 06:30
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B
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Difficulty:
85%
(hard)
Question Stats:
46% (01:59) correct
54%
(02:06)
wrong
based on 165
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What is the remainder when \((13^{100} + 17^{100})\) is divided by 25?
A. 0
B. 2
C. 4
D. 5
E. 11
Are You Up For the Challenge: 700 Level Questions
A. 0
B. 2
C. 4
D. 5
E. 11
Are You Up For the Challenge: 700 Level Questions
28 Dec 2021, 07:37
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This question can be done by Euler's theorem.
if we apply Euler’s theorem on \(\frac{13^{100}}{25}\), we will get E(25)=20. It means \(\frac{(13^5)^{20}}{25}\) will give 1 as the remainder. Applying the same to\( \frac{17^{100}}{25}\), we will get 1 as the remainder.
= \(\frac{13^{100}}{25}\) + \( \frac{17^{100}}{25}\)
= \(\frac{(13^5)^{20}}{25}\) + \(\frac{(17^5)^{20}}{25}\)
= 1+1
= 2
The answer will be B
if we apply Euler’s theorem on \(\frac{13^{100}}{25}\), we will get E(25)=20. It means \(\frac{(13^5)^{20}}{25}\) will give 1 as the remainder. Applying the same to\( \frac{17^{100}}{25}\), we will get 1 as the remainder.
= \(\frac{13^{100}}{25}\) + \( \frac{17^{100}}{25}\)
= \(\frac{(13^5)^{20}}{25}\) + \(\frac{(17^5)^{20}}{25}\)
= 1+1
= 2
The answer will be B
General Discussion
26 Apr 2025, 12:36
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