# Number 365

First of all, the great number of 365, which determines the number of days in the year. When divided by 7 it gives a remainder of 1. This is insignificant, it would seem, a feature of 365 is of great importance for our seven-day calendar. From it depends what every ordinary (non-leap) year ends with the day of the week, as it had begun. If, for example, New Year's Day was a Monday, the last day of the year and will be on Monday. At the same time, next year will start on Tuesday. Another feature of 365 is not associated with the calendar: 365 = 10x10 + 11x11 + 12x12. That is, 365 is the sum of the squares of the three consecutive numbers, starting with 10:

10² + 11² + 12²=100 + 121 + 144 = 365.

But that's not all. This same result is equal to the sum of the squares of two of the following numbers 13 and 14:

13² + 14²=169 + 196 = 365.

This property of 365 based S.A. Rachinskogo task that is depicted in the famous painting "Difficult task", Bogdanov-Belsky:

10² + 11² + 12² + 13² + 14²/365.

There is not a lot of numbers in the gallery of arithmetic wonders.