Prove that the P power minus one of 2 is prime, then p is prime

Prove that the P power minus one of 2 is prime, then p is prime

2 Λ P-1 = (2 Λ (p-1) 1) (2 Λ (p-1) - 1), there must be 2 Λ (p-1) - 1 = 1, then p = 2 is prime

It is proved that the 32nd power of 2 plus 1 is not prime

2^32+1=4294967297=641×6700417
Fermat number: 2 ^ (2 ^ n) + 1
Only when n = 0,1,2,3,4 are prime numbers
When n = 5, 2 ^ (2 ^ 5) + 1 = 641 × 6700417
When n = 6, 2 ^ (2 ^ 6) + 1 = 274177 × 67280421310721

RT equation can be calculated
the more , the better!

1. To complete a tunnel project, team a needs a day, team B needs B days. If both teams are working at the same time, it will take - days?
2. The distance between port a and port B is s. if the speed of a ship from port a to port B is V1 and the speed of a ship from port B to port a is V2, then the average round-trip speed of the ship is -?
3. When x takes what number, does the following fraction make sense?
1/(x-1)(2x+6)
4. (1) for a project, if team a completes it in t days, what is the daily workload of the team?
(2) If the price of a commodity is a yuan after X% reduction, how much is the original price of the commodity?
5. (1) what is the value of X?
(2) When real numbers a and B satisfy what conditions, the value of fraction (a-b) / (a + 1) is 0?
6. (1) when a = - 1, - 2, - 3 How does the value of fractional 1 / a change?
(2) When a is an integer, the value of fraction 6 / A is an integer?
To complete a tunnel project, team a needs a day, team B needs B days. If two teams construct at the same time, it needs - AB / (a + b) - days?
2. The distance between port a and port B is s. if the speed of a ship from port a to port B is V1 and the speed from port B to port a is V2, then the average round-trip speed of the ship is 2v1v2 / (V1 + V2) -?
3. When x takes what number, does the following fraction make sense?
1/(x-1)(2x+6)
X is not equal to 1, X is not equal to - 3
4. (1) for a project, if team a completes it in t days, what is the daily workload of the team?
1/t
(2) If the price of a commodity is a yuan after X% reduction, how much is the original price of the commodity?
a/(1-x%)
5. (1) what is the value of X?
X is any real number
(2) When real numbers a and B satisfy what conditions, the value of fraction (a-b) / (a + 1) is 0?
A = B is not equal to - 1
6. (1) when a = - 1, - 2, - 3 How does the value of fractional 1 / a change?
It's getting bigger
(2) When a is an integer, the value of fraction 6 / A is an integer?
a=-6,-3,-2,-1,1,2,3,6

Given a (0,3), B (- 1,0), C (3,0), find the coordinates of point D, so that the quadrilateral ABCD is a right angle trapezoid (a, B, C, D are arranged counterclockwise)

As shown in the figure, a (0, 3), B (- 1, 0), C (3, 0), to make the quadrilateral ABCD a right angle trapezoid (a, B, C, D arranged counterclockwise), if point D is the case shown in the figure, let D (x, y), ad = (x, Y-3), CD = (x-3, y), from the quadrilateral ABCD as a right angle trapezoid, we can get: ad · CD = 0, and | OD | = 32. That is to say, X (x-3) + y (Y-3) = 0 ①, and X2 + y2 = 32 ② =3. Therefore, the coordinates of point D which makes the quadrilateral ABCD a right angled trapezoid (a, B, C, D arranged counterclockwise) are (3, 3). If ad ⊥ AB, then the linear equation of ad is y = - 13X + 3, and the linear equation of CD is y = 3x-9. The simultaneous solution of D (185, 95) is obtained

The maximum distance from the point on the circle x ^ 2 + y ^ 2 = 1 to the line 3x-4y + 10 = 0 is

3

If we know the parabola C: X & # 178; = 4Y, if the line L passing through M (- 1,0) intersects with the parabola C at two points E and F,
Let's go through E and F to make the tangent line of parabola L &;, L &; when l &; ⊥ L &;, we can find the equation of straight line L

The line L: y = ax + a passing through M (- 1,0)
Intersecting with X & # 178; = 4Y, the equation of intersection is: X & # 178; = 4ax + 4a, that is: X & # 178; = 4ax + 4a,
X & # 178; - 4ax - 4A = 0, there must be two intersections: 16A ^ 2 + 16A > 0, that is: a > 0 or A0 or a

If the solution of the equation (2-k) x = 2013-x about X is a positive integer, then the integer k =?
If the solution of the equation (2-k) x = 2013-x about X is positive, then the real number k satisfies?

By solving the equation (2-k) x = 2013-x about X, we get that:
x=2013/(3-k)
Because the solution is positive, then 2013 / (3-K) > 0
The solution is k < 3

What is the condition that "the sum of the distances between a moving point and two fixed points in the plane is a certain value"?
Is it necessary or not?
Sufficient or unnecessary?
Necessary and sufficient?
No, no?

The necessity is not enough!
For example, when the distance is exactly equal to the distance between two fixed points, the trajectory is a line segment!
On the contrary, it is the first definition of ellipse!

Explore the mystery in the table below and fill in the blanks
Explore the secrets in the table below and fill in the blanks
Factorization of two root quadratic trinomials of quadratic equation of one variable x2-2x + 1 = 0, X1 = 1, X2 = 1, x2-2x + 1 = (x-1) (x-1) x2-3x + 2 = 0, X1 = 1, X2 = 2, x2-3x + 2 = (x-1) (X-2) 3x2 + X-2 = 0, X1 = 1=
23,x2=-1 3x2+x-2=3（x-
23）（x+1） 2x2+5x+2=0 x1=-
12,x2=-2 2x2+5x+2=2（x+
12）（x+2） 4x2+13x+3=0 x1=
,x2=
4x2+13x+3=4（x+
）（x+
）Factorize 3x & # 178; - 6x-1 with your findings

The law of this series of formulas is: first use formula method to find out X1 and X2, and then do factorization

How many days are there from September 18, 2009 to December 28, 2012?

From September 18, 2009 to September 18, 2012 is three years. February 2012 is a leap month, so the number of days in these three years is 365 + 365 + 366 = 1096. From September 18, 2012 to December 18, 2012 is three months. The number of days in these three months is 30 days in September, 31 days in October and 30 days in November, so the number of days in these three months is 30 + 31 + 30 = 912