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how is 33+23 = 35?in the above article it is given that xn + yn is divisible by x+y if n is odd through an example of 33+23 = 35 which is divisible by (3+2). how is any of that possible.
? Related: Number Systems - Introduction
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how is 33+23 = 35?in the above article it is given that xn + yn is div...
Explanation of 33+23 = 35 and Divisibility
To understand how 33+23 can equal 35 and be divisible by (3+2), we need to look at the concept of divisibility when dealing with number systems.
Divisibility Rules for x+y
- When we have two numbers x and y, their sum (x+y) can be a factor of their sum (xn+yn) only if n is odd.
- In the case of 33+23 = 35, we have x=3, y=2, n=1. Since n is odd (1 is an odd number), the sum of the digits (3+2) can indeed be a factor of the sum of the numbers (33+23).
Explanation of 33+23 = 35
- When we add 33 and 23, we get 56, not 35. So, the statement that 33+23=35 is incorrect.
- However, if we consider the correct sum of 56, we can see that 56 is divisible by (3+2) which equals 5.
Conclusion
- While the initial statement of 33+23=35 is not accurate, the concept of divisibility by x+y when n is odd holds true in number systems.
- Understanding these rules can help in simplifying calculations and identifying patterns in numbers.
To understand how 33+23 can equal 35 and be divisible by (3+2), we need to look at the concept of divisibility when dealing with number systems.
Divisibility Rules for x+y
- When we have two numbers x and y, their sum (x+y) can be a factor of their sum (xn+yn) only if n is odd.
- In the case of 33+23 = 35, we have x=3, y=2, n=1. Since n is odd (1 is an odd number), the sum of the digits (3+2) can indeed be a factor of the sum of the numbers (33+23).
Explanation of 33+23 = 35
- When we add 33 and 23, we get 56, not 35. So, the statement that 33+23=35 is incorrect.
- However, if we consider the correct sum of 56, we can see that 56 is divisible by (3+2) which equals 5.
Conclusion
- While the initial statement of 33+23=35 is not accurate, the concept of divisibility by x+y when n is odd holds true in number systems.
- Understanding these rules can help in simplifying calculations and identifying patterns in numbers.
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