Table of Contents
- 1 What is the largest positive integer n such that n 3 100?
- 2 What is the sum of all the digits of the largest positive integer n for which n 3 2006 is divisible by n 26?
- 3 What is the largest positive integer n such that?
- 4 What’s the largest negative integer?
- 5 IS 888 a perfect cube?
- 6 What is the cube of any odd number?
- 7 What is the sum of consecutive integers from N to N?
- 8 What is the sum of the first n numbers?
What is the largest positive integer n such that n 3 100?
By division we find that n3+100=(n+10)(n2−10n+100)−900. i.e. mod n+10: n≡−10 ⇒ f(n)≡f(−10) by the Polynomial Congruence Rule. Thus the largest such n occcurs when n+10 is the largest divisor of f(−10).
What is the sum of all the digits of the largest positive integer n for which n 3 2006 is divisible by n 26?
There are 11 pairs in total, namely (0,10), (1,9),…,(10,0). 30. Ans: 6. (3a + 2b + 7) + (3a + b + 7) = (a + 14) + (a + 7) + (2a + 7).
What is the largest positive integer n such that?
∴ The largest positive integer is 12.
What is the smallest positive integer whose cube ends in 888?
88 – this narrows down to ALL numbers whose cubes end in 888, which are 19,44,69,94.
What are the possible remainders when a cube is divided by 9?
Hence there are just three possible remainders 1, 8 and 0. cube of any number can be represented as 9n+x^3 where x is 0 to 8. So dividing it by 9, will give remainder as dividing x^3 by 9. for different values of x, the remainder will be 0,1, or 8.
What’s the largest negative integer?
-1
The greatest negative integer is -1.
IS 888 a perfect cube?
The value of cube root of one is 888. The nearest previous perfect cube is 729 and the nearest next perfect cube is 1000 . Cube root of 888 can be represented as 3√888.
What is the cube of any odd number?
The Cube of odd numbers is always odd. A perfect cube does not end with 2 zeroes.
What is the sum of positive integers?
The Sum of Positive Integers Calculator is used to calculate the sum of first n numbers or the sum of consecutive positive integers from n 1 to n 2 . The sum of the first n numbers is equal to:
What is the smallest number divisible by 10^5 and sum of digits?
Input : N = 5 Output : 500000 500000 is the smallest number divisible by 10^5 and sum of digits as 5. Input : N = 20 Output : 29900000000000000000000 Recommended: Please try your approach on {IDE} first, before moving on to the solution. To make a number divisible by we need at least N zeros at the end of the number.
What is the sum of consecutive integers from N to N?
The sum of the first n numbers is equal to: n(n + 1) / 2. The sum of consecutive positive integers from n 1 to n 2 is equal to: n 1 + (n 1 + 1) + + n 2 = n 2(n 2 + 1) / 2 – n 1(n 1 – 1) / 2.
What is the sum of the first n numbers?
The sum of the first n numbers is equal to: n (n + 1) / 2 The sum of consecutive positive integers from n 1 to n 2 is equal to: n 1 + (n 1 + 1) +… + n 2 = n 2 (n 2 + 1) / 2 – n 1 (n 1 – 1) / 2
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