Question

what is the remainder when 61^64846 is divided by 63?​

Answer 1

it cannot be answered

it's undefined

Answer 2

Solution :-

→ 61⁶⁴⁸⁴⁶ / 63

→ (63 - 2)⁶⁴⁸⁴⁶ / 63

When this is divided by 63, all terms with 63 will be completely divisible by 63 and remainder will be the last term (-2)⁶⁴⁸⁴⁶ .

So,

→ (-2)⁶⁴⁸⁴⁶ / 63

→ [{(-2)⁶}¹⁰⁸⁰⁶ * (-2)⁴] / 63 { This can be written as (-2)^(6k + 4) | 63 ]

→ [(64)¹⁰⁸⁰⁶ * (-2)⁴] / 63

→ {(64)¹⁰⁸⁰⁶ / 63} * {(-2)⁴ / 63}

→ 1 * 16

→ 16 (Ans.)

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