GeeksForGeeks

Question

Which of the following statement(s) is/are correct?

1. 1 is the remainder when 7^700 is divided by 100.
2. 1 is the remainder when 7^26 is divided by 100.
3. 2 is the remainder when 7^35 is divided by 13.

Comments

Thank you sumit :)

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other method 

 7$^1$  /  13   = 7  ----(1)

7$^2$  / 13    = 49 /13 = 10 --(2)

$7^3 / 13$  = 7*10 / 13 =  5  ---(3)

$7^4 / 13$ = 5*7 / 13  = 9  ----(4)

$7^5 / 13$ = 7*9 = 63/13 = 11  ----(5)

$7^6 / 13$ = 11*7 = 77/13 =  -1   or  12  // we conclude that           7^12  / 13   will be  =  +1 

cycle of 12  divide 35/12  we got remainder  remainder = 11  , so 

we have to find $\frac{7^{11}}{13}$

= multiply equation $(1)\times (2)\times (3)\times (5)$

 $7\times 10\times 5\times11 = \frac{3850}{13} = \boldsymbol{2}$

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can you pls tell me the method name which you have used!!