If a is a natural number, is a4-3a2 + 9 prime or composite? Give your proof

If a is a natural number, is a4-3a2 + 9 prime or composite? Give your proof

The original formula = (A4 + 6A2 + 9) - 9A2 = (A2 + 3A + 3) (a2-3a + 3), when a = 0, the original formula = 9 is a composite number; when a = 1, the original formula = 7 is a prime number; when a = 2, the original formula = 13 is also a prime number; when a > 2, A2 + 3A + 3 > 1, a2-3a + 3 = (A-2) (A-1) + 1 > 1, which shows that a4-3a2 + 9 can be divided into
If a is a natural number, is a ^ 4-3a + 9 prime or composite?
It's all possible
A = 1, a ^ 4-3a + 9 = 7 are prime numbers
A = 2 A ^ 4-3a + 9 = 19 is prime
A = 3 A ^ 4-3a + 9 = 81 is a composite number
A = 4 A ^ 4-3a + 9 = 253 = 11 * 23 is a composite number
uncertain:
1. When a = 0, a ^ 4-3a + 9 = 0 ^ 4-3 × 0 + 9 = 9 is a composite number
2. When a = 1, a ^ 4-3a + 9 = 1 ^ 4-3 × 1 + 9 = 7 is prime
Known: A is a natural number, ask a & # 8308; - 3A & # 178; + 9 is prime or composite?
a⁴-3a²+9
=(3 - 3 a + a^2) (3 + 3 a + a^2)
So it's total!
a⁴-3a²+9
=(a²-3)²
Therefore, when a = 2, a & # 8308; - 3A & # 178; + 9 = 1 is neither prime nor composite.
When a is not equal to 2, it is a composite number. But if it is a complete square difference, shouldn't - 3A & # 178; be true? Wrong.
x⁴- 3x² + 9
=X & # 8308; + 6x... Expand
a⁴-3a²+9
=(a²-3)²
Therefore, when a = 2, a & # 8308; - 3A & # 178; + 9 = 1 is neither prime nor composite.
When a is not equal to 2, it is a composite number. Question: but if it is a complete square difference, shouldn't - 3A & # 178; be - 6A & # 178; Tenable?
The least composite number and the least prime number have only one common factor
There is only 1, the smallest composite number 4, the smallest prime 1, so the common factor of two numbers is 1
How are prime numbers and composite numbers divided? Are they divided according to whether the individual bit is prime or composite number, or according to how many divisors the whole has?
Prime number (also known as prime number) is that in all integers larger than 1, except 1 and itself, there is no other divisor. This kind of integer is called prime number or prime number. It can also be said that prime number has only 1 and its own two divisors. This final rule is only a literal explanation. Can there be an algebraic formula to specify the one represented by letters
Prime number and composite number
Prime number is a positive integer which can not be divided by other numbers except 1 and itself
The difference between prime number and composite number lies in the number of factors
Except 1,0, positive integers that are not prime numbers are composite numbers
0 and 1 are neither prime nor composite numbers
What are prime numbers and composite numbers?
1 to 1000
Prime table
2 3 5 7 11 13 17 19 23 29
31 37 41 43 47 53 59 61 67 71
73 79 83 89 97 101 103 107109 113
127 131 137 139 149 151 157 163 167 173
179 181 191 193 197 199 211 223 227 229
233 239 241 251 257 263 269 271 277 281
283 293 307 311 313 317 331 337 347 349
353 359 367 373 379 383 389 397 401 409
419 421 431 433 439 443 449 457 461 463
467 479 487 491 499 503 509 521 523 541
547 557 563 569 571 577 587 593 599 601
607 613 617 619 631 641 643 647 653 659
661 673 677 683 691 701 709 719 727 733
739 743 751 757 761 769 773 787 797 809
811 821 823 827 829 839 853 857 859 863
877 881 883 887 907 911 919 929 937 941
947 953 967 971 977 983 991 997 228
3.5.7.9
2.4.6.8
Prime number can only be expressed by the product of itself and 1 (of course, it is limited to integers). In addition to the product of itself and 1, sum number can also be expressed in other ways. For example, 9 can be written as 1 × 9 or 3 × 3. 1 is both prime and composite. Ask: I know
Which of the following numbers are prime numbers and which are composite numbers? Fill in the specified circle respectively. 1 & nbsp; & nbsp; 13 & nbsp; & nbsp; 27 & nbsp; 41 & nbsp; & nbsp; 57 & nbsp; & nbsp; 61 & nbsp; & nbsp; 73 & nbsp; & nbsp; 84 & nbsp; & nbsp; 9547 & nbsp; & nbsp; 11 & nbsp; & nbsp; 15 & nbsp; & nbsp; 33 & nbsp; & nbsp; 49 & nbsp; & nbsp; 51 & nbsp; & nbsp; 63 & nbsp; & nbsp; 87 & nbsp; & nbsp; & nbsp; 99 I found that:______ .
By classification, we can find that 1 is neither prime nor composite
Which of the following numbers are prime numbers and which are composite numbers?
13、27、41、57、61、73、84、95、11、15、33、49、51、63、87、99
13. 41, 61, 73 and 11 are prime numbers
27=3×9、57=3×9、84=4×21、95=19×5、15=3×5、33=11×3、49=7×7、51=3×17、
63 = 7 × 9, 87 = 3 × 29, 99 = 9 × 11 are composite numbers
13, 41, 61, 73, 11 are prime numbers
Everything else is a sum
Which of the following numbers are prime numbers? Which are composite numbers?
29 27 31 39 43 49 57 1 67 83 91 97
Prime number:
Total number:
Prime numbers: 29, 27, 31, 43, 67, 83, 97
Total: 39, 49, 57, 91
1 is neither prime nor composite