How many numbers can be taken from natural numbers 1 to 100 so that the sum of any four numbers can be divided by 15

How many numbers can be taken from natural numbers 1 to 100 so that the sum of any four numbers can be divided by 15

These are the numbers
15,30,45,60,75,90
6 in total

In any four natural numbers, are there two of them whose difference can be divided by 3?
ditto

Natural numbers can be divided into three categories
Divide by three, divide by three, divide by one, divide by three, divide by two,
Therefore, any four numbers, there must be two numbers of the same class, their difference is divided by three
The proof is complete

Find the sum of all natural numbers that can be divisible by 13 and 1 within 1000

1+14+27+… ＋… ＋976＋989＝1＋（14＋989）×38＝38115

How many natural numbers between 1000 and 2000 can be divided by 6, 8 and 10 at the same time?
Do me a favor!

3*8*5=120
2000/120=16.6666
1000/120=8.3333
120*9=1080
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.
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120*16=1920
8 in total