Indian National Mathematics Olympiad 2013 Problem 2

[MGEditz]

Good job, keep posting more videos 😄👍 on Math Olympiad...

[zubiiiiii_]

You also couldve done it a little faster: (5:44) since 4k+3 | k+13 then 4k+3<=k+13 which yields to k<=3 and its easy to check that only for k=1

[chowkungchow]

I can't follow 'one of them must divide the other at 4:32.'

[KarlFredrik]

Me: working on the problem for 2 days without solving. Let's think critically smacks out a solution in less than 11 min.

[EscobarColombie]

On peut écrire m^2+3=3p^x et 4m+1=p^y avec x+y=n ou inversement.
Puis on montre que pg d (m^2+3, 4m+1) divise 49 et qui est égal à p^inf(x, y).
P est alors égal 7. On étudie les caa pgcd = 1, 7, 7^2. On trouve la même solution
Pour le cas m^2+3 =p^× 4m+1=3p^y : même raisonneent pas de solutions

[bosorot]

simplier is just do mod 3 to 4m^3+m^2+12m+3 . before factor it out . you will find that m is multipication of 3 . ( and not m=3k+2 . which make problem twice of work to do )) . let m=3k . put it back will get (3k^2+1)(12k+1)=p^n .