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For example, 5 has a remainder of 1 and is equal to 1 squared + 2 squared but 7 which has a remainder of 3 is not a sum of two squares.
Take the discovery by Fermat, the 17th-century French mathematician, that a prime number that has a remainder of 1 after division by 4 (like 41) can always be written as the sum of two square numbers (41=16+25).
Inoculation of T-lymphoblast cells with prepubertal primate testis cells still has a remainder of 0.1% of tumor cells after FACS sorting for CD90+(THY-1+) and CD45−, and the remaining tumor cells were able to form tumors after transplantation to nude mice [ 90].
If we use such a calculator for our example, we can see that 3100/100 has a remainder of 1.
Again, this number has a remainder of 4. Put the 6 on top of the 4 and the remainder for in small writing in between the 4 and 7. Again, you have v=created a new number of 47. 47 divided by 5 is 9 and again, it has a remainder.
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Those having a remainder of 1 are sums of two squares (in a unique way), and those having a remainder of 3 are not.
And by limiting future century leap years to those divisible by 900 and which have a remainder of 200 or 600, we have become correct to one day in 44,000 years!
If you have a remainder from step 7, that is also part of the answer.
5 × 2 = 10, which is two less than twelve, so we say that we have a remainder of two (or R2).
If you still have a remainder after using the final digit, add a ".0" to the dividend and a "." to your quotient, so you can bring down another digit and continue.
18/6 — since we know that 18 is just 6 × 3, we know we'll have a remainder of 0, so we don't need to worry about the fraction part of our mixed number.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com