Remainder 50^56^52/11 ??
@vbhvgupta said:Remainder 50^56^52/11 ??
I am not solving this by Euler method ..
Write the given number as (55-5)^....1
55 is div by 11 and remaining part is -5^....1
Any power of 5 ends with 5 . So remainder is -5 or 6
Write the given number as (55-5)^....1
55 is div by 11 and remaining part is -5^....1
Any power of 5 ends with 5 . So remainder is -5 or 6
@vbhvgupta said:am getting 6
E(11)= 10
So try to express 56^52 in terms of 10k+R 56^52 mod 10 = 6^52 mod 10
= 6 * 6^51 mod 10
= 3*6^51 mod 5
=3
multiply by 2 u get 6. So R=6
question reduces to 50^(10k+6) mod 11
= 50^6 mod 11
=6^6 mod 11
=36^3 mod 11
= 3^3 mod 11
= 5
So try to express 56^52 in terms of 10k+R 56^52 mod 10 = 6^52 mod 10
= 6 * 6^51 mod 10
= 3*6^51 mod 5
=3
multiply by 2 u get 6. So R=6
question reduces to 50^(10k+6) mod 11
= 50^6 mod 11
=6^6 mod 11
=36^3 mod 11
= 3^3 mod 11
= 5
@vbhvgupta said:Remainder 50^56^52/11 ??
e(11) is 10
56^52%10 = 6
50^6%11 = 6^6%11 = (-5)^6%11 = 25^3%11 = 3^3%11 = 27%11 = 5
@vbhvgupta
Should be 5..
E(11)= 10..Thus, (56^52) Mod 10 = 6..
Thereby, (50^6) Mod 11 = (6^6) Mod 11 = (7^2) Mod 11 = 5..
@bs0409 said:Lets try 32^32^32 mod 7E(7)=6
@Ibanez said:E(11)= 10
@Logrhythm said:e(11) is 1056^52%10 = 6
@mailtoankit said:5?E(11)=10
Got the concept....thnks
please tag me in new questions!
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@PURITAN said:@vbhvgupta ans 22D*K1 +14=ND*K2 +8 =3ND*(K1+K2) + 22 =4N WHERE K=REM
@mailtoankit said:22?n=dq+143n=dq1+84n=d(q+q1)+22
Even me. I guess 22. Puys what can be divisor - 44 right? Just out of curiosity.....
If the option contained 0, then?
my approach:
N = DA + 14
3N = DB+8
Now, 3N = 3*DA+14*3 = 3DA+52
But the remainder is 8, then divisor or multiple of divisor is 44. As remainder is 14, then divisor has to be greater than 14, only 22 or 44 satisfies as divisor.
if 44 is the divisor, then 22 is the answer.
if 22 is the divisor, then 0 can be the answer.
If the option contained 0, then?
my approach:
N = DA + 14
3N = DB+8
Now, 3N = 3*DA+14*3 = 3DA+52
But the remainder is 8, then divisor or multiple of divisor is 44. As remainder is 14, then divisor has to be greater than 14, only 22 or 44 satisfies as divisor.
if 44 is the divisor, then 22 is the answer.
if 22 is the divisor, then 0 can be the answer.