03 Nov '14 22:21

Here's a problem from elementary number theory:

Let A and B be integers such that A > B > 0.

The last three digits are the same in the decimal representations of

1978^A and 1978^B. What is the minimum value C = A + B ?

Advice: One needs some basic knowledge of number theory, particularly of

modular arithmetic. Having that, this problem does not require any deep

insight, only determined manipulation with perhaps a touch of cleverness.

If someone's interested in this problem and lacks any knowledge of number

theory, then I would not object to one consulting Wikipedia, YouTube (if it

turns you on), or even a textbook (gasp!) to learn some basic concepts.

I lack the time to comment upon every detail of everyone's attempted

solution, yet I shall confirm a correct solution or post one myself after a

fair amount of time has elapsed.

Good luck to everyone who's willing to make an honest effort.

Let A and B be integers such that A > B > 0.

The last three digits are the same in the decimal representations of

1978^A and 1978^B. What is the minimum value C = A + B ?

Advice: One needs some basic knowledge of number theory, particularly of

modular arithmetic. Having that, this problem does not require any deep

insight, only determined manipulation with perhaps a touch of cleverness.

If someone's interested in this problem and lacks any knowledge of number

theory, then I would not object to one consulting Wikipedia, YouTube (if it

turns you on), or even a textbook (gasp!) to learn some basic concepts.

I lack the time to comment upon every detail of everyone's attempted

solution, yet I shall confirm a correct solution or post one myself after a

fair amount of time has elapsed.

Good luck to everyone who's willing to make an honest effort.