what is the remainder of (27^639 + 54^349)/28
Answers
Given : (27⁶³⁹ + 54³⁴⁹)/28
To Find : remainder
Solution:
27⁶³⁹ + 54³⁴⁹
= 27⁶³⁹ + (27 x 2)³⁴⁹
= 27⁶³⁹ + 27³⁴⁹ x 2 ³⁴⁹
= 27³⁴⁹ (27²⁹⁰ + 2³⁴⁹)
27⁶³⁹ /28
= (28 - 1)⁶³⁹ /28
Hence remainder = (- 1 )⁶³⁹ = - 1
as all other terms divisible by 28
54³⁴⁹
= (27 x 2)³⁴⁹
= 27³⁴⁹ x 2 ³⁴⁹
27³⁴⁹ remainder = (- 1)³⁴⁹ = -1
2³⁴⁹ = (2⁵)⁶⁹.2⁴
2⁵ = 32 32 mod 28 = 4 = 2²
4⁶⁹.2⁴
= 2¹⁴²
= (2⁵)²⁸.2²
= 2⁵⁶.2²
=(2⁴)¹⁴.2²
= 2²⁸.2²
= (2⁴)⁷.2²
= 2¹⁴.2²
= (2⁴)⁴
= 4⁴
= 2⁸
= (2⁴)²
= 4²
= 16
54³⁴⁹ / 28 Remainder
= -1 * 16
= -16
Total remainder = - 1 - 16 = -17
Hence remainder = -17 + 28
= 11
(27⁶³⁹ + 54³⁴⁹)/28 remainder = 11
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Answer:
Step-by-step explanation:
