whta is the method that is bng used for solving 29 question.. by time..
Remainder of lcm. of 3^2003-1 and 3^2003+1... as in how come it is (3^2-1)/2
They have just crapped out in the solution.
The right approach is to find the remainder by 20 ( if we find remainder by 10 , we cant be sure of the last digit when we divide by 2 subsequently , as 8 can give last digit of 4 or 9 ) for the product of those 2 nos. and then divide that remainder by 2.
The right approach is to find the remainder by 20 ( if we find remainder by 10 , we cant be sure of the last digit when we divide by 2 subsequently , as 8 can give last digit of 4 or 9 ) for the product of those 2 nos. and then divide that remainder by 2.
Remainder was 8 , and hence answer is 4.
Can someone post the question that you are referring to?
Que : To find Last Digit (LD) of LCM [3^2003-1 and 3^2003+1] Soln : LD ( LCM [ 3^3 - 1 and 3^3 + 1]) ...... taking last digit of 2003 in the power, i.e., 3 LD ( LCM [ 26 and 28]) LD ( 13*7*4 ) = LD (264) = 4 Answer
Que : To find Last Digit (LD) of LCM [3^2003-1 and 3^2003+1] Soln : LD ( LCM [ 3^3 - 1 and 3^3 + 1]) ...... taking last digit of 2003 in the power, i.e., 3 LD ( LCM [ 26 and 28]) LD ( 13*7*4 ) = LD (264) = 4 Answer
The right approach is to find the remainder by 20 ( if we find remainder by 10 , we cant be sure of the last digit when we divide by 2 subsequently , as 8 can give last digit of 4 or 9 ) for the product of those 2 nos. and then divide that remainder by 2.
Remainder was 8 , and hence answer is 4.
the other way by which i did is... i found out the last 2 digits by dividing 3^2003 by 100 .. which yields the last 2 digits as 27 so the numbers are 26 and 28 ... n it can b done easily ;) 26*28 /2 which gives 4
Ques: 7^777 / 28 Soln : 7^7 / 28 ............ taking last digit of power i.e., 7 By cyclicity of 7^n / 28 .... it comes like 7..21..7..21..7..21........n So, the cyclicity of 7^n / 28 is 2. Hence, for 7^7 / 28, remainder is 7 .......
Ques: 7^777 / 28 Soln : 7^7 / 28 ............ taking last digit of power i.e., 7 By cyclicity of 7^n / 28 .... it comes like 7..21..7..21..7..21........n So, the cyclicity of 7^n / 28 is 2. Hence, for 7^7 / 28, remainder is 7 .......
still dint get u dude.. please explain in a simpler way..i am not able to understand the cyclicity.. ..7...21 .. 7.. 21.. what is that actly?
still dint get u dude.. please explain in a simpler way..i am not able to understand the cyclicity.. ..7...21 .. 7.. 21.. what is that actly?
When you will divide, 7^1/28 = 7 remainder 7^2/28 = 21 7^3/28 = 7 7^4/28 = 21 It shows that, for every odd power of 7 when divided by 28 yeilds 7 as remainder and every even power of 7 when divided by 28 yeilds 21 as remainder. From this, after performing only 3 operation you can make out that 7^7/28 = 7 (as the power on 7 is odd)