1. 3^302 mod 5
Solution:
`3^302" mod "5`
Here `3^302=(3^2)^151`
`=(3^2" mod "5)^151" mod "5`
`=(9" mod "5)^151" mod "5`
`=4^151" mod "5`
Here `4^151=(4^2)^75*4`
`=(((4^2" mod "5)^75" mod "5)*(4" mod "5))" mod "5`
`=(((16" mod "5)^75" mod "5)*4)" mod "5`
`=((1^75" mod "5)*4)" mod "5`
`=((1" mod "5)*4)" mod "5`
`=(1*4)" mod "5`
`=4" mod "5`
`=4`
This material is intended as a summary. Use your textbook for detail explanation.
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