You need a bigger calculator
find the smallest positive integer b which satisfies 3^56=b(mod7)
I am very new to modular arithmetic and I stubbled upon this question.
Wouldn't 'b' have a specific solution.
Asking for the smallest positive integer b confuses me.
when I put 3^56 into my calculator or into Excel i get a rounded answer. This also surprised me a little.
The calculator doesn't have enough digits, so there is no enigma there.
But why does Excel round? I think the last digit has to be 1, and excel just gives about 15 places and then a stack of zeros.
Can you set excel to give more acuracy? I guess that this is a second question.
This is it for me. would someone like to add input please.
I responded to you in the wee hours but I must not have pressed 'reply'
I was thinking of writing Santa a note, but now Dan has shown me I don't have to.
(Unless I am visiting the regional Australia where there is no internet coverage.)