Divisors of Large Numbers: Upper Secondary Mathematics Competition Question

Find those single-digit integers greater than 1 that divide evenly into 79⁷⁹+1.

Also, find the highest value of n such that 10ⁿ divides evenly into 79⁷⁹+1.

As always, questions such as these should be done without a calculator. I think this question should take approximately 5 minutes.






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