Hardest math question

also 99999999999999999999999999999999999999999999999999999999999999999999999999999999999 cubed times 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

If you'll grant me euler's formula, it is easy.

e^(ix)=cos(x)+i*sin(x) (eulers formula)

let x=pi

e^(i pi)= cos(pi)+i*sin(pi)

observe: cos (pi) = -1

               sin (pi) = 0

thus e^(i pi) = -1 + i*0 = -1.

Name 3 euler theorems don’t look on the internet etc.

Comment 22 answer: all those numbers ^ 4

Nvm

Prove that there exists a Hadamard matrix for every positive multiple of 4.

999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999994089094508349505999999999999999999999999999999999999999999999999999999999999999309203902193093092109309329230923092130930392109231903120931290999999999999999^454343999999999999999999999999999999999999999999999999999999999999999999999999999999329808210391230832974837878479289202222222232322312139999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999*888

Prove that there are infinitely many twin primes

=

9999999999999999999999999999999999999999999999999999999999999999999999999999999999699999999999999999999999999999999999999999999999999999999000000000000000000000000003000000000000000000000000000000000000000000000000000000029999999999999999999999999989999999999999999999999999999999999999999999999999999999700000000000000000000000000000000000000000000000000000000000000000000000000000000001

(388 digits)

To solve this, use a free online calculator like: Big Integer Calculator.

Here is a Quanta Magazine article about some impressive problems being solved in number theory, including work by Oxford mathematician and Fields Medal winner James Maynard.

• A New Generation of Mathematicians Pushes Prime Number Barriers

https://projecteuler.net/ has some nice problems. https://projecteuler.net/problem=656 is a nice one.

Prove that the collatz conjecture holds for all integers.

prove fermat's last theorem

💀

If f(x)=xe^x then find the limit of (f^-1(x)/logx) when x->inf and domain of f(x) is (0,inf)

what is the last digit of e (eulers number)

hahahahahahahahh Imbiciles

its already proved

https://www.scienzamedia.uniroma2.it/~eal/Wiles-Fermat.pdf

warning: google says its dangerous to visit so;

1 my friend, 1

i was trying to use Lambert W function for xe^x but realized that would get me nowhere

2 x 50% of 9^ 284593559374584

Wait that’s just 9^284583559374584

Nice, simple modular arithmetic. Ones place is just mod 10. Can use euler's totient function.
phi(10) = 10(1-1/2)(1-1/5) = 4
47^2020 (mod10) is congruent to 47^0 (mod10). Ans: 1