Find Divisor...Math?
A number when divided by a divisor leaves a remainder of 16. When twice the original number is divided by the same divisor, the remainder is 7. What would the divisor be?
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answers:
Steve4Physics say: No equations are necessary.

The divisor must be greater than 16.

Doubling the number initally doubles the remainder from 16 to 32.

But since the remainder is only 7, the divisor must be 32 - 7 = 25.
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Φ² = Φ+1 say: a mod n = 16 and 2a mod n = 7
a = kn + 16 and 2a = jn + 7
a + 9 = (j - k)n where k>j, n>16

16 mod 25 = 16 and 32 mod 25 = 7
41 mod 25 = 16 and 82 mod 25 = 7
66 mod 25 = 16 and 132 mod 25 = 7

Looks like a pattern, but the divisor here is consistently 25.
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the internet say: 16 * 2 = 32
32 - 7 = 25
let's try 25 as a divisor.

We want it easy.
To get a remainder or 16,
we add 16 to the divisor and get
something like 41.
41 / 25 -> remainder is 16 looks good.
now 41*2 = 82
82 = 3 * 25 + 7 looks even better
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