如何求解除以16余10的整数？大数计算遇难题

Hey there! Let's cut through the confusion here—you don't need complex number theory theorems to figure this out, it's all about recognizing a simple pattern.

The Universal Formula for These Numbers #

Every number that leaves a remainder of 10 when divided by 16 fits this basic expression:
16k + 10
where k is any non-negative integer (0, 1, 2, 3, ... you get the idea).

Let's test this with the examples you already know:

• When k=0: 16*0 +10 =10 → Correct, 10 ÷16 leaves remainder 10.
• When k=1: 16*1 +10=26 → Also correct, 26-16=10.

For larger numbers, just keep plugging in bigger values of k:

• k=5: 16*5+10=90 → 90 ÷16=5 with remainder 10 (16*5=80, 90-80=10)
• k=100: 16*100+10=1610 → 1610 ÷16=100 with remainder 10, no issues here.

Why Larger Numbers Might Be Tripping You Up #

If you're having trouble verifying bigger numbers, it's almost certainly a calculation error when you're dividing by 16 to check the remainder. Here's a quick hack to make verification easier:
Take the number you're checking, subtract 10 from it. If the result is cleanly divisible by 16 (no remainder), then your original number fits the bill.

For example:

• Let's check 1242: 1242-10=1232. 1232 ÷16=77, no remainder → So 1242 leaves remainder 10 when divided by 16.
• If you tried 1234: 1234-10=1224. 1224 ÷16=76.5 → Not an integer, so this one doesn't work.

Quick Verification Trick #

If you're using a calculator or code, you can use the modulo operator (%) to check instantly:
For any number X, if (X - 10) % 16 == 0, then X is exactly the kind of number you're looking for.

That's all there is to it—no fancy math required, just a simple pattern and quick checks to confirm!

内容的提问来源于stack exchange，提问作者sumit goyal