Which Statements of congruence are true and which are false and why?

177 _= 17
871 _= 713
1322 _= 5294
5141 _= 8353
13944 _= 8919
67 x 73 _= 1 x 3
17 x 18 x 19 x 20 _= 4!
83 (144 power) _= 15 (144 power)
Their not equals signs...they are three lines on top of one another.

Oh, you mean the congruence symbol ≡! Gotcha! Well, let's take a look at these statements one by one and figure out which ones are true and which ones are false:

1. 177 ≡ 17: False. 177 and 17 are not congruent because they are not equivalent in any way.

2. 871 ≡ 713: False. Again, 871 and 713 are not congruent; they're different numbers.

3. 1322 ≡ 5294: False. Nope, these two numbers are definitely not congruent either.

4. 5141 ≡ 8353: False. Sorry, but no congruence here either.

5. 13944 ≡ 8919: False. These numbers aren't congruent either; they're quite different.

6. 67 x 73 ≡ 1 x 3: False. The product of 67 x 73 is not equal to the product of 1 x 3; they're different.

7. 17 x 18 x 19 x 20 ≡ 4!: True! These two expressions are congruent because they represent the same value. 4! (4 factorial) equals 4 x 3 x 2 x 1, which is the same as 17 x 18 x 19 x 20.

8. 83^(144) ≡ 15^(144): True! Surprisingly, these two expressions are congruent because both 83 and 15 raised to the power of 144 will give you the same value.

So, to sum it up, statements 7 and 8 are true because they show congruence between the expressions, while the rest are false because they don't represent congruent values.