Which one of the following numbers is exactly divisible by (1113 + 1)?
1152 - 1
Put x = 11¹³. Then \(11^{52}-1=x^4-1=(x+1)(x-1)(x^2+1)\), so it is divisible by 11¹³+1. Modulo x+1, 11³⁹−1 has remainder −2 and 11²⁶+1 has remainder 2. Also \(11^{33}+1\equiv11^7+1\), which is positive and smaller than the divisor. Thus only 11⁵²−1 qualifies.
Important Questions from Divisibility and Remainder
If all positive divisors of 132 are arranged in descending order, then what digit will be at unit place of first divisor ?
If 3 2019 is divided by 10, then what is the remainder?
The number 3798125P369 is divisible by 7. What is the value of the digit P?
Consider all 3-digit numbers (without repetition of digits) obtained using three non-zero digits which are multiples of 3. Let S be their sum.
Which of the following is/are correct?
1. S is always divisible by 74.
2. S is always divisible by 9.
select the correct answer using the code given below:
How many 3-digit natural numbers (without repetition of digits) are there such that each digit is odd and the number is divisible by 5?
