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Hi can anyone explain and and the q plzzz

Answer»

Question:Let a(n)= 6^n + 8^n. Determine the REMAINDER upon DIVIDING a(83) by 49.

Final Answer : 35.
For STEP by step calculation see pic.
Solution:
Steps:
1) Expressing the numbers in terms of 7.
2) Remainder of 83 * 7 by 49 is 35 .

a(83) = {6}^{83} + {8}^{83} \\ = > {(7 - 1)}^{83} + {(7 + 1)}^{83} \\ by \: binomial \: expansion \: \\ = >2(83c(0) {7}^{83} + 83c(2) {7}^{81} + \\ ...... + 83c(82) {7}^{1} ) \\\\a(83) \: (mod \: 49) = > \\ 2(0 + 0 + ...83 \times 7(mod49)) \\ = > 0 + 0 + ...35 \\ = > 35

For Proper Calculation of Binomial Expansion see Pic.


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