Congruences and Euler's Formula

[bigp0ppa1046]

find a number "a" that satisfies the folowing three properties:

(i) a is congruent to 7^3003 (mod 3750)
(ii) a is b/w 1 and 5000
(iii) and is not divisible by 7

Can anyone help?? I am so lost in this class and need to pass this course so that i can graduate in may!

 

[Denis]

Well, 7^3003 (mod 3750) = 343.

 

[daon]

According to requirements ii and iii, it must be between 1 and 5000 and not divisible by 7. 343 meets ii, but not iii. The only other option is 4093 which fits all three.

edit: I'm still wondering what this has to do with Euler's Formula?

 

[bigp0ppa1046]

it was just the section that the problem was found under. I dont know other than that.