give me answer show that one and only one out of n,n+4,n+8,n+12 and n+16 is divisible by 5, where n is any positive integer
To be evenly divisible by 5, the number must end in 0 or 5. If n is an integer, one and only one of that set of numbers can end in 0 or 5.
To determine which one out of the given numbers (n, n+4, n+8, n+12, n+16) is divisible by 5, we need to observe a pattern in divisibility with respect to 5.
The pattern is that the last digit of a number determines its divisibility by 5. If the last digit of a number is either 0 or 5, then the number is divisible by 5.
Let's analyze each number in the given list:
1. n: As n is any positive integer, we cannot determine its last digit or divisibility by 5 without more information. Therefore, n may or may not be divisible by 5.
2. n+4: To determine the divisibility of n+4 by 5, we need to consider the last digit of n+4, which is the same as the last digit of n. If the last digit of n is either 1, 6, or any number that ends with 1 or 6 in its one's place, then n+4 will not be divisible by 5 since its last digit will not be 0 or 5.
3. n+8: Similar to the previous case, to check the divisibility of n+8 by 5, we need to consider the last digit of n. If the last digit of n is either 2, 7, or any number ending in 2 or 7, then n+8 will not be divisible by 5.
4. n+12: To determine the divisibility of n+12 by 5, we need to consider the last digit of n in the same way as before. If the last digit of n is either 3, 8, or any number ending in 3 or 8, then n+12 will not be divisible by 5.
5. n+16: Lastly, to determine the divisibility of n+16 by 5, we need to consider the last digit of n. If the last digit of n is either 4 or 9, or any number ending in 4 or 9, then n+16 will not be divisible by 5.
From the analysis of each number, we observe that the only possibility for a number in the list to be divisible by 5 is if the last digit of n ends with either 0 or 5. Therefore, the only number in the given list that will be divisible by 5 is n itself.
In conclusion, only the number n out of the given numbers (n, n+4, n+8, n+12, n+16) will be divisible by 5 if the last digit of n is either 0 or 5.