# A remainder problem.

• May 29th 2012, 03:32 AM
Megamind
A remainder problem.
Okay, I quite didn't know which category of question this belongs to, I genuinely expect you to pardon my ignorance.
So here is the question:

What is the remainder obtained when the number (1010 )^1 + (1010 )^2 + (1010)^3 + .... so on till + (1010)^10 is divided by 7.

Read (1010)^1 as 10 to the power of (10 to the power of 1)
''
^2 as 10 to the power of (10 to the power of 2)

and so on.
• May 29th 2012, 06:47 AM
Soroban
Re: A remainder problem.
Hello, Megamind!

$\text{What is the remainder when the number}$
. . $10^{(10^1)} + 10^{(10^2)} + 10^{(10^3)} + \hdots + 10^{(10^{10})}\,\text{ is divided by 7 ?}$
. . $\left(10^{10} + 10^{100} + 10^{1,000} + \hdots + 10^{10,000,000,000}\right) \div 7$