keresztszám

Keresztszám is a Hungarian term that translates to "cross number" or "digit sum." It is a fundamental concept in number theory and digital root calculations. The keresztszám of a non-negative integer is the sum of its digits. For example, the keresztszám of 123 is 1 + 2 + 3 = 6. If the sum of the digits is a single digit, that is the final keresztszám. If the sum is a multi-digit number, the process is repeated until a single digit is obtained. This single digit is also known as the digital root. For instance, the keresztszám of 987 is 9 + 8 + 7 = 24. Since 24 is not a single digit, we repeat the process: 2 + 4 = 6. Therefore, the digital root of 987 is 6.

The keresztszám has several interesting properties. It is congruent to the original number modulo 9. This means that a number and its keresztszám will have the same remainder when divided by 9. For example, 123 divided by 9 has a remainder of 6, and its keresztszám, 6, also has a remainder of 6 when divided by 9. This property is often used in divisibility tests, particularly for checking divisibility by 9. A number is divisible by 9 if and only if its keresztszám is 9 (or 0 if considering the digital root which is usually mapped to 1-9, with 0 being equivalent to 9 in this context). The concept is also related to casting out nines, a method for verifying arithmetic calculations. In some contexts, the keresztszám is used in numerology or recreational mathematics.