CODEWITHSUNDEEP
pythonmodular-arithmetic
AJ Burnett
AJ Burnett

Reputation: 33

Python and Modular Arithmetic

Suppose a and b are odd integers. Then a^2 + b^2 is either 2 or 10 modulo 16. My question is the following: Is there a way of writing a script whose assumptions are a%2 == 1 and b%2 == 1 so that the output (a^2 + b^2) % 16 gives the tuple (2,10)? Edit: Here's my unsuccessful approach:

def test():
aList=[]
bList=[]
for a in range(0,16):
    for b in range(0,16):
        if a%2==1 and b%2==1:
            aList.append(a)
            bList.append(b)
            print  a^2+b^2%16

This of course will not return a tuple. My hope is to output the tuple (2,10).

Upvotes: 0

Views: 225

Answers (1)

kaya3
kaya3

Reputation: 51142

As I understand, you want to collect the distinct residues modulo 16 of a**2 + b**2 (note the ^ operator is not what you want here) into a tuple. So instead of printing each residue out, you should add them to a set in order to collect the distinct values. The set can then be converted to a tuple, using sorted to get them in order:

residues = set()
for a in range(0, 16):
    for b in range(0, 16):
        if a % 2 == 1 and b % 2 == 1:
            residues.add((a**2 + b**2) % 16)

residues = tuple(sorted(residues))
print(residues)

The result is (2, 10) as expected.

This code can be simplified somewhat: instead of generating all integers in the range and just keeping the odd ones, you can generate odd integers using a range starting from 1 with a step size of 2; and you can use a set comprehension for brevity.

residues = {
    (a**2 + b**2) % 16
    for a in range(1, 16, 2)
    for b in range(1, 16, 2)
}

residues = tuple(sorted(residues))
print(residues)

Upvotes: 3

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