Math Major Examples -- Number Theory #7

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[TimL_]

It would be convenient if you included these example videos in the playlist, as I assume a lot of people will be using that to follow the course. Thanks for all the great work.

[schweinmachtbree]

Euler's theorem requires the base and the modulus to be coprime, not the base and the exponent, so in the last problem the relevant conditions are that 11/12/15 respectively are/aren't/aren't relatively prime to 100, not 1000. (although of course in this case these are equivalent)

[richardschreier]

4:28 N₃=1365 (not 1395). This leads to x=1701.

For the egg problem, the first five congruences are equivalent to x ≡ −1, so x ≡ −1 (mod 6!). x = 119 is the smallest natural number that works. Since 119 is divisible by 7, we are done.

For the 3-thieves problem, each container had x = 3193 ge of rice, so 2x-16 = 9563 ge of rice were stolen and the thieves took 3192, 3179 and 3192 ge, respectively.