Consecutive division by different number

The difference between the squares of two consecutive numbers is 31. Find the numbers.

Out of 25 consecutive natural numbers, two numbers can be chosen in lambda ways such that their "sum" is divisible by 2 . Then lambda//36 is.

The difference between the square of any two consecutive integers is equal to (a) sum of two numbers (b) difference of two numbers (c) an even number (d) product of two numbers

Property: Product of r consecutive number is divisible by r!

Prove that the product of any three consecutive even natural numbers is divisible by 16.

The sum of four consecutive even numbers is 23 more than the sum of three consecutive odd numbers. The difference between the lowest even and the highest odd number is 3. Find the sum of the four consecutive even number.

Two consecutive natural numbers are respectively divisible by 4 and 7. The sum of their respective quotient is 8. Find the sum of between the numbers.