1. Determine the unknown digit in the units place of the number 401512* so that the remainders when this number is divided by 3 and by 5 are equal.
Solution. The unknown digit can be 5, 6, or 7. By dividing the resulting number by 3 and by 5, we will ensure that in the first case, the number is divisible by both 3 and 5, in the second case, the remainders when divided by 3 and 5 are 1, and in the third case, the remainders when divided by 3 and 5 will be 2.