Infinity on High finished the year at number twenty-one on IFPI's list of the "Top 50 Global Best Selling Albums of 2007". "Infinity on High" has shipped over two million copies worldwide. The album also charted inside the top five worldwide, making it the band's most successful and breakthrough album internationally. "Infinity on High" charted all over Europe, debuting at number eight on "Billboard"'s European Albums chart. In Australia, it debuted at its peak of number four on the Australian ARIA Albums Chart. It remained on the Australian chart for a total of fifty weeks, spending its first seven weeks in the top
Jacobi symbol Jacobi symbol The Jacobi symbol is a generalization of the Legendre symbol. Introduced by Jacobi in 1837, it is of theoretical interest in modular arithmetic and other branches of number theory, but its main use is in computational number theory, especially primality testing and integer factorization; these in turn are important in cryptography. For any integer "a" and any positive odd integer "n", the Jacobi symbol is defined as the product of the Legendre symbols corresponding to the prime factors of "n": where is the prime factorization of "n". The Legendre symbol is defined for all integers "a" and all