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AURORKA [14]
3 years ago
5

There is more than one integer greater than 1 which leaves a reminder of1 when divided by each of the four smallest primes

Mathematics
1 answer:
Vlad1618 [11]3 years ago
4 0

Answer:

210

Complete question found at brainly(ID): 18678557 is stated below.

There is more than one integer, greater than 1, which leaves a remainder of 1 when divided by each of the four smallest primes. What is the difference between the two smallest such integers?

Step-by-step explanation:

Prime numbers are numbers that can only be divided by itself and 1

The smallest of the prime numbers we have = 2, 3, 5, 7

Since the integers greater than 1 are said to be divided by the four smallest prime numbers, we would assume the number of integers are 4 in total.

Let the integers be T

From the question:

Integer/(prime number) = quotient + (remainder/prime number)

Integer/(prime number) = Q + R/P

Let the different quotients derived from all 4 prime number = w, x, y, z

For prime 2:

T/2 = w + 1/2

T/2 - 1/2 = w

(T-1)/2 = w

T = 2w + 1

T-1 = 2w

Following the above solution

For prime 3:

T = 3x + 1

T-1 = 3x

For prime 5:

T = 5y + 1

T-1 = 5y

For prime 7:

T = 7z + 1

T-1 = 7z

T-1= T-1 = T-1 = T-1

2w = 3x = 5y = 7z

T-1 = LCM of all the prime numbers

T- 1 = 2×3×5×7

T-1 = 210

T = 210+1 = 211

T = 211

The smallest of the integer greater than 1 that leaves a remainder of 1 = 1(T-1) + 1 = 211

The next after the smallest number: 2(T-1) +1= 2(210) + 1 = 421

The two smallest number = 1(T-1) + 1 and 2(T-1) +1 respectively

The difference between the two smallest such integers = 421-211 = 210

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What other information do you need to prove ΔABE is congruent to ΔEDA by SSS?
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To prove ΔABE is congruent to ΔEDA by SSS we need that EAC should be an equilateral triangle.

What is an equilateral triangle?

A triangle is said to be equilateral if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.

Here, we have

AEC is a triangle in which B∈ AC and D∈ EC

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Now, we have to prove that :

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Hence, to prove ΔABE is congruent to ΔEDA by SSS we need that EAC should be an equilateral triangle.

To learn more about the equilateral triangle from the given link

brainly.com/question/15294703

#SPJ4

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