Arithmetic pattern $1 + 2 = 3$, $4 + 5 + 6 = 7 + 8$, and so on The other interesting thing here is that 1,2,3, etc appear in order in the list And you have 2,3,4, etc terms on the left, 1,2,3, etc terms on the right This should let you determine a formula like the one you want Then prove it by induction
Newest arithmetic-derivative Questions - Mathematics Stack Exchange A conjecture about binary palindromes and arithmetic derivatives Corrected question From the sequence of binary palindromes A006995 (eg 1001001001001) the sequence of possible gaps between consecutive palindromes contain the elements:
arithmetic - Is a negative number squared negative? - Mathematics Stack . . . When you have $-3$ entered in to a calculator, then you press a button to square the current value, you are effectively performing $ (-3)^2= (-3)* (-3)=9$ If, in a calculator or computer program you enter $-3^2$ the precedence of the operations is interpreted as $- (3^2)=-9$
Manageable project to learn some arithmetic geometry I think one more arithmetic direction this can go is to prove the (easier parts of) the Weil conjectures for smooth curves over finite fields These conjectures motivated massive amounts of algebraic geometry, and are very down to earth, its all just counting solutions to equations over finite fields!
No infinite arithmetic progression exists with prime numbers 8 There are arbitrarily long sequences of consecutive composites The well known proof: look at $$ k!+2, k!+3, \ldots, k! + k $$ So no arithmetic progression can contain only primes