Funny Series
Number Theory
Level
1
let ,
A[1] = 1
A[i] = A[i-1]+(i-1)+i [i>1]
A[102596325845] % 10 = ?
Details and assumptions :-
M % N means the remainder when M is divided by N.
The answer is 5.
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1st you need to recognize the pattern.
A[1] = 1 = 1^2
A[2] = 1 + (2-1) + 2 = 1 + 1 + 2 = 4 = 2^2
A[3] = 4 + (3-1) + 3 = 4 + 2 + 3 = 9 = 3^2
A[4] = 9 + (4-1) + 4 = 9 + 3 + 4 = 16 = 4^2
....
A[i] = i^2
... A[102596325845] = 102596325845^2 = 102596325845 * 102596325845 ...
Now you need to know about modulus theory of multiplication
(a * b)%m = ( (a%m) * (b%m) )%m
Here a = 102596325845 , b = 102596325845 and m = 10
So
(102596325845 * 102596325845)%10
= ( (102596325845%10) * (102596325845%10) )%10
= (5 * 5)%10
= 25%10
= 5