My Day!

Number Theory Level 2

If today is Saturday, what day is 1 0 20 10^{20} days from now?

Thursday Tuesday Monday Friday

Hans Lawrence Dela Cruz by Hans Lawrence Dela Cruz , 25, Philippines

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

4 solutions

Adarsh Srinivasan
Sep 12, 2014

10^5=2(mod 7); 10^20=2^4(mod 7); 10^20=16(mod 7); 10^20=(2 mod 7); hence 2 days from saturday ie monday

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Duc Anh
Aug 1, 2014
  • 10 = 3 mod 7
  • 1 0 2 10^{2} = 3 2 3^{2} mod 7 = 2 mod 7
  • 1 0 20 10^{20} = 2 10 2^{10} mod 7 = 1024 mod 7 = 2 mod 7
0 Helpful 0 Interesting 0 Brilliant 0 Confused
Mohamed Akl
Aug 1, 2014

hhhhhhhhhhhhhhhhh > i did not know how to solve and i choose by chance :v

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Hemang Sarkar
Jul 24, 2014

10^6 is 1(mod 7). so, 10^20 is 100 mod7. or, 2(mod 7).

0 Helpful 0 Interesting 0 Brilliant 0 Confused

i don't know those (mod) stuffs :D help me please! :)

Hans Lawrence Dela Cruz - 6 years, 10 months ago

Log in to reply

srsly????????????????

Jayakumar Krishnan - 6 years, 10 months ago

Log in to reply

yes, i actually solve that using binomial expansion.

Hans Lawrence Dela Cruz - 6 years, 10 months ago

First divide 10^{20} by 7, as there is seven days in a week, which equals to 1.4285714 i.e. approx 1 and the first day ina week is monday and bingo!!!

Vishal Barman - 6 years, 10 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...