The remainder when 5power500 when it is divided by 13 - Maths - Mathematical Reasoning

Question

The remainder when 5power500 when it is divided by 13

Shruti Tyagi · Accepted Answer

Dear Student,

we need to find that when 5500 is divided by 13 what is remainder
we know that 513, remainder =5when 5213=2513 remainder=12when 5313=12513 remainder=8when 5413=62513 remainder=1  since 13×48=624hence we know that every cycle of 54 will have remainder 1now we have 5500=54×125⇒54125Hence remainder when 5412513= 1125 ⇒1Thus when 5500 is divided by 13 we get remainder as 1

Regards,

The remainder when 5power500 when it is divided by 13...