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.
This is quite a technical subject and source material can be viewed at the link below.
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When expressed as a ratio of two integers (not intergers!), the simplest form for the integer but not others, has 1 as the denominator.
-5 is an integer and a rational number. Integers can be positive or negative. Rational numbers can be expressed as a fraction of integers.
Any integer can be expressed as a fraction. The simplest is the integer itself divided by one.
The statement is false.
Any integer that is divisible by 2 with no remainder is even otherwise it is an odd 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.
-5 is an integer and a rational number. Integers can be positive or negative. Rational numbers can be expressed as a fraction of integers.
Positive integers are greater than zero. Negative integers are less than zero.
That can be expressed as -4 < [|x|] < 3. Those integers are -3, -2, -1, 0, 1, and 2.
Any integer can be expressed as a fraction. The simplest is the integer itself divided by one.
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.
As 6 is a positive integer, no negative integer is greater than it.
The statement is false.
56.25% is not an integer and so cannot be expressed as a sum, difference, product or quotient of consecutive integers.
1024
No, it is an integer; all integers are rational.
No. All integers are rational numbers, since an integer like the number 5 can be expressed as a fracion 5/1.