If the relationship between the nth term of series {an} and its previous term or terms can be expressed by a formula, then this formula is called the recurrence formula of this series.
If a number can be expressed as the square of an integer, it is called a complete square number. A complete square number is nonnegative, and a complete square number has two terms.
If a positive integer A is the square of an integer B, then this positive integer A is called a complete square number. Zero can also be called a complete square number.
If the square of an even number must be divisible by 4; Any odd square divided by 4 (or 8) is 1, that is, the number divided by 4 by 2 or 3 must not be a complete square number.
When the single digit of a complete square number is odd, the number on the tenth digit must be even. When the single digit of a complete square number is 6, its ten digits must be odd.
A natural number whose single digit is 5 but the last two digits are not 25 is not a complete square number; A natural number with only odd zeros at the end is not a complete square number; The unit number is 1, 4, 9, and the natural number with odd ten digits is not a complete square number.
Except the number 1, after a complete square number decomposes prime factors, the exponents of all prime factors are even. If a number is decomposed and all indexes are even, then it must be a square number. The total number of all factors of a complete square number is odd. A natural number with an odd factor must be a complete square number.
The first two terms and the last two terms are squared, twice the product of the first two terms and the last two terms are placed in the middle, and the symbol follows the center. (that is, calculate the powers of two terms separately, then calculate the product of two terms, multiply by 2, and then put this number in the middle of the powers of two numbers. The symbol between the preceding numbers follows the symbol in the middle of the original formula, with+for the complete sum of squares formula,-for the complete difference of squares formula, and+for the following symbols).
In number theory, a prime factor refers to a prime number that can be divisible by a given positive integer. According to fundamental theorem of arithmetic, regardless of the arrangement order, every positive integer can be expressed as the product of its prime factors in a unique way. Two positive integers without homogeneous factors are called coprime. Because 1 has no prime factor, 1 is coprime with any positive integer (including 1 itself). A positive integer with only one prime factor is a prime number.