Find the largest six-digit number, for which each digit, starting with the third, is equal to the sum of the two previous digits.
Find the largest number of which each digit, starting with the third, is equal to the sum of the two previous digits.
Find a two-digit number that is 5 times the sum of its digits.
Find numbers equal to twice the sum of their digits.
Which five-digit numbers are there more of: ones that are not divisible by 5 or those with neither the first nor the second digit on the left being a five?
Peter recorded an example of an addition on a board, after which he replaced some digits with letters, with the same figures being replaced with the same letters, and different figures with different letters. He did it such that he was left with the sum: \(CROSS + 2011 = START\). Prove that Peter made a mistake.
Prove that amongst numbers written only using the number 1, i.e.: 1, 11, 111, etc, there is a number than is divisible by 1987.
Prove that there is a power of 3 that ends in 001.
How many six-digit numbers exist, the numbers of which are either all odd or all even?
Prove that the product of any three consecutive natural numbers is divisible by 6.