Number Theory | When does a linear congruence have a solution??

We give the proof of a proposition regarding linear congruences and their solvability.

[programstix]

This and prior video out of order in this short playlist "Modular Arithmetic and Linear Congruences" FYI. Much appreciated videos!!

[SanketAlekar]

Loving these videos. In the Modular Arithmetic and Linear Congruences Playlist, this video (#7) should be before #6 (Linear Congruences Proposition 2)

[paulkohl]

Thanks Michael Penn for doing this and the other number theory videos. Very clear presentation of relevant math. Good

[georgesadler]

professor Penn, thank you for a powerful demonstration on When does a linear congruence have a solution.

[sgssergio]

Great video!!
Why do you probe k values up to 3?
There is a general form to perfom a solutions of this type of congruences without probe all possiblities of k? For large numbers is very tediuos. Thanks!!

[johnagbaabah]

Great job! I find this helpful. Numbering your videos would help a great deal.

[PunmasterSTP]

Another phenomenal video; again, thanks so much for making and posting these!

[ogglieostrich]

Why do you only check up to k=3. Shouldn't it be up to k=17?

[priyanshpandey]

Cant we solve linear congruence by ax=b(modm) which implies ax-b=mk(k€natural no) then rearranging as ax-mk=b and solving this diophantine equation.

[putin_navsegda]

7:06 cant get why it's a(ym) is congruent to b mod m? Shouldn't it be b congruent to aym mod m?