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Legendre's proof relating to Hexagonal Numbers and the significance of the number 1791 has been improved upon by Duke and Schulze-Pillot (1990) to just three hexagonal numbers for every sufficiently large integer.
There are 13 positive integers within the range 5 to 130 that cannot be represented by only 4 hexagonal numbers. Only the integers 11 and 26 require 6 hexagonal numbers.
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What is the difference between a rational number that is not an integer and a rational number that is an integer?
When expressed as a ratio of two integers (not intergers!), the simplest form for the integer but not others, has 1 as the denominator.
Is -5 an integer and an rational number?
-5 is an integer and a rational number. Integers can be positive or negative. Rational numbers can be expressed as a fraction of integers.
Can integers include fractions?
Any integer can be expressed as a fraction. The simplest is the integer itself divided by one.
When comparing two integers the integer with the bigger absolute value is always the greater integer?
The statement is false.
What are the odd integers greater than 40?
Any integer that is divisible by 2 with no remainder is even otherwise it is an odd integer
What is the difference between a rational number that is not an integer and a rational number that is an integer?
When expressed as a ratio of two integers (not intergers!), the simplest form for the integer but not others, has 1 as the denominator.
Is -5 an integer and an rational number?
-5 is an integer and a rational number. Integers can be positive or negative. Rational numbers can be expressed as a fraction of integers.
What is a positive integer and what is a negtive integer?
Positive integers are greater than zero. Negative integers are less than zero.
Can integers include fractions?
Any integer can be expressed as a fraction. The simplest is the integer itself divided by one.
What set of integers greater than -4 and less than 3?
That can be expressed as -4 < [|x|] < 3. Those integers are -3, -2, -1, 0, 1, and 2.
When comparing two integers the integer with the greater absolute value is always the greater integer?
No.A positive integer is always larger than a negative integer. In the case of two negative integers, the integer with the larger absolute value is actually smaller.
What are all negative integers greater than 6?
As 6 is a positive integer, no negative integer is greater than it.
When comparing two integers the integer with the bigger absolute value is always the greater integer?
The statement is false.
What is 56.25 percent as a consecutive integers?
56.25% is not an integer and so cannot be expressed as a sum, difference, product or quotient of consecutive integers.
What is the only integer between 1000 and 2000 which cannot be expressed as the sum of consecutive integers?
1024
How do you determine the value of one integer in comparison to the value of another integer?
Look at the places that integers have on the number line. The integer that is on the right is greater that the integer is on the left.
Are any integers irrational?
No. All integers are rational numbers, since an integer like the number 5 can be expressed as a fracion 5/1.
