I. Determine the remainder when14^(1000) is divided by 13
2. Determine theremainder when 12^(1001) is divided by 13.
3. Determine theremainder when 5’^(30) is divided by 31.
4. Show that 2(5n+1) + 5(n+2) is divisible by 27 for any positive integern.
(use modular arithmetic if possible)
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