We are interested to see divisibility checking of only prime numbers in base 10. For a prime P, you need to find the smallest positive integer N such that P's divisibility testing is "N-sum" or "N-alterum". Remember divisibility testing of 3 in base 10? It was simple, right? We need to add all the digits and then check if it is divisible by 3. Call this method "1-sum". • In case of testing of 11, we need to add all digits by alternating their signs. For example,1354379988104 = 11*123125453464 and (4- 0+1-8+8-9+9-7+3-4+5-3+1) = 0, which is divisible by 11 (0 = 0*11). Let's call this method "1-altersum". • In case of 7, we need to add all 3-digit-groups by alternating their signs. For example, 8618727529993 = 7*1231246789999 and (993- 529+727-618+8) = 581, which is divisible by 7 (581 = 7*83). Similarly, we call this method "3-altersum". In similar Manner, 13's checking is "3.altersum"
We are interested to see divisibility checking of only prime numbers in base 10. For a prime P, you need to find the smallest positive integer N such that P's divisibility testing is "N-sum" or "N-alterum". Remember divisibility testing of 3 in base 10? It was simple, right? We need to add all the digits and then check if it is divisible by 3. Call this method "1-sum". • In case of testing of 11, we need to add all digits by alternating their signs. For example,1354379988104 = 11*123125453464 and (4- 0+1-8+8-9+9-7+3-4+5-3+1) = 0, which is divisible by 11 (0 = 0*11). Let's call this method "1-altersum". • In case of 7, we need to add all 3-digit-groups by alternating their signs. For example, 8618727529993 = 7*1231246789999 and (993- 529+727-618+8) = 581, which is divisible by 7 (581 = 7*83). Similarly, we call this method "3-altersum". In similar Manner, 13's checking is "3.altersum"
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![We are interested to see divisibility checking of only prime numbers in
base 10. For a prime P, you need to find the smallest positive integer N
such that P's divisibility testing is "N-sum" or "N-alterum".
Remember divisibility testing of 3 in base 10? It was simple, right?
We need to add all the digits and then check if it is divisible by 3.
Call this method "1-sum".
In case of testing of 11, we need to add all digits by alternating their
signs. For example,1354379988104 = 11*123125453464 and (4-
0+1-8+8-9+9-7+3-4+5-3+1) = 0, which is divisible by 11 (0 = 0*11).
Let's call this method "1-altersum".
In case of 7, we need to add all 3-digit-groups by alternating their
signs. For example, 8618727529993 = 7*1231246789999 and (993-
529+727-618+8) = 581, which is divisible by 7 (581 = 7*83). Similarly,
we call this method "3-altersum". In similar Manner, 13's checking is
"3-altersum".
Develop a C++ program that solve the above problem, sample input output
is listed below.
Input:
1
78
Output:
Case 1: 77-altersum](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3378fec4-95e0-4fe8-a4be-ba5a3452b034%2Fd11577dc-db95-46a3-a0ee-203ba4a678e2%2Fv3jot1o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:We are interested to see divisibility checking of only prime numbers in
base 10. For a prime P, you need to find the smallest positive integer N
such that P's divisibility testing is "N-sum" or "N-alterum".
Remember divisibility testing of 3 in base 10? It was simple, right?
We need to add all the digits and then check if it is divisible by 3.
Call this method "1-sum".
In case of testing of 11, we need to add all digits by alternating their
signs. For example,1354379988104 = 11*123125453464 and (4-
0+1-8+8-9+9-7+3-4+5-3+1) = 0, which is divisible by 11 (0 = 0*11).
Let's call this method "1-altersum".
In case of 7, we need to add all 3-digit-groups by alternating their
signs. For example, 8618727529993 = 7*1231246789999 and (993-
529+727-618+8) = 581, which is divisible by 7 (581 = 7*83). Similarly,
we call this method "3-altersum". In similar Manner, 13's checking is
"3-altersum".
Develop a C++ program that solve the above problem, sample input output
is listed below.
Input:
1
78
Output:
Case 1: 77-altersum
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