That precisely sums up this problem which was also posted on ascent4cat.
What is unit digit for 7 exp 11 exp 22 exp 33 ?
i.e., 7 raised to 11 raised to 22 raised to 33 .. phew ..!!
And, the answer so simply put by one indra goel as follows :)
The powers of 7 have the following unit places (starting from 7^1) 7,9,3,1,7,9... so at every 5th power there is repetition, therefore we can remove all the 5's from the power terms(power mod 5) and see the remainder to get the units place...In this problem 7 exp 11 exp 22 exp 33..11 mod 5=1..22 mod 5=2..33 mod 5=3..multiplying the power remainders(1*2*3) we get 6 which further gives 6 mod 5=1 thus finally we have the number 7 in the units place as per the pattern we generated
Good one .. :)
I LOVE numbers :)
What is unit digit for 7 exp 11 exp 22 exp 33 ?
i.e., 7 raised to 11 raised to 22 raised to 33 .. phew ..!!
And, the answer so simply put by one indra goel as follows :)
The powers of 7 have the following unit places (starting from 7^1) 7,9,3,1,7,9... so at every 5th power there is repetition, therefore we can remove all the 5's from the power terms(power mod 5) and see the remainder to get the units place...In this problem 7 exp 11 exp 22 exp 33..11 mod 5=1..22 mod 5=2..33 mod 5=3..multiplying the power remainders(1*2*3) we get 6 which further gives 6 mod 5=1 thus finally we have the number 7 in the units place as per the pattern we generated
Good one .. :)
I LOVE numbers :)