MathDB

11

Part of 2017 QEDMO 15th

Problems(2)

[(2^1+3^1)...(2^{2048}+3^{2048})+2^{4096}]/3^{4096}

Source: 15th -a QEDMO problem 11 (19. - 22. 10. 2017) https://artofproblemsolving.com/community/c1512515_qedmo_2005

5/30/2021
Calculate (21+31)(22+32)(24+34)(28+38)...(22048+32048)+2409634096\frac{(2^1+3^1)(2^2+3^2)(2^4+3^4)(2^8+3^8)...(2^{2048}+3^{2048})+2^{4096}}{3^{4096}}
Sumalgebra
f (xy) = f (x) f (y) , f (x) =x^{-1} for more than 3/4 of members of finite gro

Source: 15th -b QEDMO problem 11 (19. - 22. 10. 2017) https://artofproblemsolving.com/community/c1512515_qedmo_2005

5/30/2021
Let GG be a finite group and f:G→Gf: G \to G a map, such that f(xy)=f(x)f(y)f (xy) = f (x) f (y) for all x,y∈Gx, y \in G and f(x)=x−1f (x) = x^{-1} for more than 34\frac34 of all x∈Gx \in G is fulfilled. Show that f(x)=x−1f (x) =x^{-1} even holds for all x∈Gx \in G holds.
algebrafunctionalfunctional equation