Remainder when (45 power 73+50 power 73) when divided by 19
Answers
Given : 45⁷³ + 50⁷³ divided by 19
To Find : Remainder
Solution:
45⁷³ + 50⁷³
= (38 + 7)⁷³ + (57 - 7)⁷³
(a + b)ⁿ = aⁿ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b² +................................+ ⁿCₙ₋₁a¹bⁿ⁻¹ + bⁿ
(38 + 7)⁷³ will have all term with
38 except 7⁷³
(57 - 7)⁷³ will have all term with
57 except (-7)⁷³
38 & 57 both are divisible by 19
now 7⁷³ + (-7)⁷³
= 7⁷³ - 7 ⁷³
= 0
Hence 45⁷³ + 50⁷³ is divisible by 19
So remainder = 0
45⁷³ + 50⁷³ divided by 19 , remainder = zero
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