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I am by no means a mathematician, but I do have a decent eye for patterns, and I found a pretty cool one today. I was hoping one of you guys could tell me more about it.

As a general rule, I've found that if (a*b) mod c = 1, then the sequence a^n mod c is the reverse of the sequence b^n mod c.

For example, (7*8) mod 11 = 1

and 7^n mod 11= 7,5,2,3,10,4,6,9,8...

while 8^n mod 11= 8,9,6,4,10,3,2,5,7...

As another example, (56*24) mod 17 =1

and 56^n mod 17 = 5,8,6,13,14,2,10,16,12,9,11...

while 24^n mod 17= 11,9,12,16,10,2,14,13,6,8,5...

What do you all think about this? I'm willing to bet that all I've done is show a simple concept in a convoluted way, but I'm to fried to think critically about this any more.

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# Playing around with the modulo operation

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