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No. Odd numbers can be written as the sum of consecutive integers, but some multiples of odd numbers are even.

Q: All multiples of odd natural number can be written as the sum of consecutive natural numbers?

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That isn't true.

A multiple of a number is that number multiplied by an integer. It is obviously not possible to get "all multiples" of any number. ================================================= There are an infinite number of multiples of any single number. Also, there are an infinite number of quantities written with a single digit. Besides the 19 whole numbers from -9 to +9, there are also all the numbers like .4 and -.0007 . So the answer to your question would consist of an infinite number of lists, with an infinite number of items on each list. We're both slightly busy at the moment. Maybe we'll get back to you.

It is 5 because 9828/6 = 1638 and 6 times 1638 = 9828

The infinite set of numbers of the form n*sqrt(2) where n is any integer. However, since sqrt(2) is one of the factors, there is no obvious reason to restrict the other factor to an integer. In that case, the answer is, at least the infinitely many numbers of the form x*sqrt(2) where x is any real number. But why restrict to real numbers? Why not include complex multiples?

It is the product, not the sum, of three consecutive integers that is divisible by 6. The three consecutive integers must be multiplied, not added.For example, 2+3+4 = 9, which is not evenly divisible by 6.If your first number is odd, then the statement works. Here's why:The first number is odd, so it can be written as 2n+1 for some integer n.The next two numbers are just 2n+2 and 2n+3.Then the sum of the three numbers is:(2n+1) + (2n+2) + (2n+3) = 6n + 6which is obviously divisible by 6 regardless of the number you used for n.For the 'Product of three consecutive integers..." see the Related Question below.

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That isn't true.

All the odd numbers.

-- All but one of them are greater than 8 . -- All but one of them are written with more than 1 digit. -- All are multiples of 4 . -- All are multiples of 2 . -- All are even numbers. -- All are positive, real, natural, integers.

All multiples of 12 are also multiples of 6 and they all can be written as the sum of nine numbers.

the numbers 0 through 9 written in sequence or any portion of that sequence

Yes.

All but 251 of them. Any odd number greater than 1 can be written in the form 2n + 1 where n = 1,2,3,... then 2n+1 = (n + 1)2 - n2 Any multiple of 4 can be written as 4n where n = 1,2,3,... then 4n = (n + 1)2 - (n - 1)2 However, unless you allow 1 = 12 - 02 1 cannot be so written as a difference of two squares and odd multiples of 2 cannot be so written. So that is the number 1 and 250 odd multiples of 2: 251 numbers in all. 1 cannot be so written.

Natural numbers are basically counting numbers including zero (0,1,2,3,4,...) Since 6.40 can be written as a fraction, no, it is not a natural number.

Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. All natural and whole numbers are rational.

Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. All natural and whole numbers are rational.

Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. All natural and whole numbers are rational.

ODD NUMBERS. If you take two consecutive whole (non zero) numbers then one will be an odd number and the other will be an even number. The sum of an odd number and an even number is always an odd number.