Number 1998 * 1998 * 1998 * *What is the remainder of the product of 1998 divided by 7?

Number 1998 * 1998 * 1998 * *What is the remainder of the product of 1998 divided by 7?

There are 2000 1998 = 7 * n + 3 in total, so the final result is the multiplication of 2000 3, that is, 3 ^ 2000 = 9 ^ 1000 = (7 + 2) ^ 1000, so it becomes the remainder of 2 ^ 1000 divided by 7. 2 ^ 1000 = 1024 ^ 100 = (146 * 7 + 2) ^ 100 becomes the remainder of 2 ^ 100 divided by 7. Similarly, it becomes the remainder of 1024 divided by 7, that is 2, so 1998 * 1998 * 1998 * *The remainder of the product of 1998 divided by 7 is 2

What is the remainder of the product of 7 × 7 × 7 ×. × 7 divided by 2?

The remainder is one
Because no matter the power of 7 is odd, you can see the product of single digits, odd times odd or odd

Find the remainder of the product of 1998 multiplied by 8,

2000 is divisible by 8
1998^1997
=(2000-2)^1998
2 to the third power is divisible by 8
1998÷3=666
There is no remainder
So the remainder of multiplying 1998 by 8 is 0
It's not easy for beginners to type,

A mathematical problem of the first two fraction equation,
If the fractional equation (a + 1) / (x + 1) = 2A has no solution, find the value of A

(a+1)=2a(x+1)
2ax=1-a
No solution
There are two cases
1、2a=0
a=0
2. The root of the equation is x = - 1
∴-2a=1-a
a=-1
A = 0 or a = - 1

The center of the ellipse C is at the origin, the focus F1 and F2 are on the x-axis, a and B are the vertices of the ellipse C, P is a point on the ellipse C, and Pf1 ⊥ x-axis, Pf1 ∥ AB are used to calculate the eccentricity

X ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 a (- A, 0) B (0, b) F1 (- C, 0) F2 (C, 0) the center of ellipse C is at the origin, the focus F1, F2 is on the X axis, a, B are the vertices of ellipse C, P is a point on ellipse C, and PF2 ⊥ X axis, Pf1 ∥ AB, P (C, B ^ 2 / a) KAB = B / akpf1 = B ^ 2 / 2acpf1 ∥ AB, B / a = B ^ 2 / 2aca = 2c, E = C / a = 1 / 2

As shown in the figure, in the triangle ABC, ∠ BAC = 90 °, ad ⊥ BC at point D, EF ⊥ BC at point F, FM ⊥ AC at point m, ∠ 1 = ∠ 2, find

For what?

Let the two complex roots of the quadratic equation 2x ^ 2 - (3m-1) x + m ^ 2 + 1 = 0 with real coefficients of X be x1, X2, and the absolute value of X1 + x2 = 3 to find M

When m = 7, the equation is x \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\forexample, X2 ∈ rx1 + x2 = (3m-1)

Given x ∈ [2,8], find the minimum and maximum of F (x) = log2 (x / 2) * log2 (x / 4)

Minimum 0
Maximum 2

A rectangular piece of hard paper with length of ACM, width of BCM and circumference of 32cm is cut out from each corner, and then folded into a small square with side length of 1cm
Lidless carton
When the length of the bottom area of the carton without cover is twice the width, find a and B

When the length is a, the width is 32 △ 2-A = 16-a
Lie equation: A-2 = (16-a-2) × 2
a=10
b=16-10=6

A calculation problem about series circuit
New year's party to install some small bulbs to increase the atmosphere, some of the existing resistance of 20 ohm, the normal luminous current of 0.3 a small bulbs, should be () such bulbs () connected in the 220 V lamp circuit

According to u = R * I, the rated voltage of small bulb is equal to 6V
The voltage and current of series circuit are equal, and the shunt voltage of parallel circuit is equal
Obviously, it is impossible to connect in series in a 220 V circuit
Series circuit voltage, so with 220 / 6 is the number of need to series
The final answer is: 37 in series