LORD ZARKON!
Question for u pls.......
2^x+3^x where x1000000, find value of x if 2^x+3^x result is divisible by 7

Question

LORD ZARKON!
Question for u pls.......
2^x+3^x where x>1000000, find value of x if 2^x+3^x result is divisible by 7

zarkon · Answer

1,000,005

zarkon · Answer

x is any number of the form $$3+(n-1)\cdot 6$$
where $$n\in\mathbb{N}$$

anonymous · Answer

OK thts what i got, did u use modulus division

anonymous · Answer

to see when integer solutions showed up

zarkon · Answer

yes...I used properties of modular arithmetic.

anonymous · Answer

is there a neater way then trial an error

anonymous · Answer

kinda like i was hoping 2^3n=8^n=(7+1)^n

zarkon · Answer

I din't use trial and error...i derived my formula and then found the smallest n such then 3+(n-1)6 was greater then 1000000 and was divisible by 7

anonymous · Answer

uh sir, how do u derive the formula without testing so man number

anonymous · Answer

many*

anonymous · Answer

cause i saw a pattern

zarkon · Answer

use 2^3 mod 7 =1

and 3^3 mod 7=6

so x= 3 is a solution

3^6 mod 7 =1
thus 3^9 mod 7=6


from this I get my formula

anonymous · Answer

uh yh kk

anonymous · Answer

thnkx once again