Question: What is the inheritance of hypophosphatemic rickets?

Context:
Among 35 candidate genes in this region, the dentin matrix protein 1 gene (DMP1) was sequenced to reveal a nonsense mutation 250C/T on exon 6. 
Previous research has shown that mutations in the DMP1 gene are responsible for autosomal recessive hypophosphatemic rickets in humans.
A novel nonsense mutation in the DMP1 gene in a Japanese family with autosomal recessive hypophosphatemic rickets.
Autosomal recessive hypophosphatemic rickets (ARHR) is an extremely rare disorder of autosomal recessive inheritance, characterized by hypophosphatemia resulting from renal phosphate wasting. 
Prenatal diagnosis for a novel splice mutation of PHEX gene in a large Han Chinese family affected with X-linked hypophosphatemic rickets.
X-linked hypophosphatemia (XLH) is the most common form of heritable rickets characterized by X-linked dominant inheritance, renal phosphate wasting, hypophosphatemia, and defective bone mineralization.
Molecular analysis of DMP1 mutants causing autosomal recessive hypophosphatemic rickets.
We previously demonstrated that the mutations Met1Val (M1V) and the deletion of nucleotides 1484-1490 (1484-1490del) in Dentin matrix protein-1 (DMP1) cause the novel disorder autosomal recessive hypophosphatemic rickets (ARHR), which is associated with elevated fibroblast growth factor-23 (FGF23).
First, we examined a kindred with a severe hypophosphatemic rickets phenotype and recessive inheritance. 
Discordance for X-linked hypophosphataemic rickets in identical twin girls.
We report monozygotic twin girls with a family history consistent with X-linked hypophosphataemic rickets (XLH). 
Microsatellite analysis was performed to confirm monozygosity and bi-parental inheritance of the X chromosome. 
Hypophosphatemia due to isolated renal phosphate wasting is a genetically heterogeneous disease. Two new genes linked to two different forms of hereditary hypophosphatemias have recently been described. Autosomal recessive form of hypophosphatemic rickets was mapped to chromosome 4q21 and identified homozygous mutations in dentin matrix protein 1 (DMP1) gene, which encodes a non-collagenous bone matrix protein.
Somatic and germline mosaicism for a mutation of the PHEX gene can lead to genetic transmission of X-linked hypophosphatemic rickets that mimics an autosomal dominant trait.
Familial hypophosphatemic rickets is usually transmitted as an X-linked dominant disorder (XLH), although autosomal dominant forms have also been observed. Genetic studies of these disorders have identified mutations in PHEX and FGF23 as the causes of X-linked dominant disorder and autosomal dominant forms, respectively.
Direct nucleotide sequencing of FGF23 and PHEX revealed that the elder daughter was heterozygous for an R567X mutation in PHEX, rather than FGF23, suggesting that the genetic transmission occurred as an X-linked dominant trait. 
Somatic and germline mosaicism for an X-linked dominant mutation in PHEX may mimic autosomal dominant inheritance.
We report two cases of x-linked dominant hypophosphatemic rickets involving a man and his daughter. 
X-linked hypophosphatemic rickets--a report of 2 cases and review of literature.
The study of this family tree strongly suggests an x-linked dominant inheritance.
Autosomal dominant hypophosphatemic rickets/osteomalacia: clinical characterization of a novel renal phosphate-wasting disorder.
We performed clinical and biochemical evaluations of individuals from a large kindred with autosomal dominant hypophosphatemic rickets/osteomalacia.
 In conclusion, autosomal dominant hypophosphatemic rickets/osteomalacia is an inherited disorder of isolated renal phosphate wasting. 
[Scriver type autosomal hypophosphatemic rachitis: a family case].
A familial observation of hypophosphatemic rickets with unusual inheritance and evolution, different from that of X linked hypophosphatemia, is reported. 
This observation is quite similar to the 'autosomal hypophosphatemic bone disease' described by Scriver et al. 
The HHRH is transmitted by autosomal recessive inheritance and is an extremely rare form of hypophosphatemic rickets.
First, we examined a kindred with a severe hypophosphatemic rickets phenotype and recessive inheritance.
A familial observation of hypophosphatemic rickets with unusual inheritance and evolution, different from that of X linked hypophosphatemia, is reported.
Autosomal recessive hypophosphatemic rickets (ARHR) is an extremely rare disorder of autosomal recessive inheritance, characterized by hypophosphatemia resulting from renal phosphate wasting.
Hereditary hypophosphatemic rickets with hypercalciuria (HHRH) is a rare disorder of autosomal recessive inheritance that was first described in a large consanguineous Bedouin kindred.
Autosomal recessive hypophosphatemic rickets (ARHR) is an extremely rare disorder of autosomal recessive inheritance, characterized by hypophosphatemia resulting from renal phosphate wasting
A familial observation of hypophosphatemic rickets with unusual inheritance and evolution, different from that of X linked hypophosphatemia, is reported
The HHRH is transmitted by autosomal recessive inheritance and is an extremely rare form of hypophosphatemic rickets
First, we examined a kindred with a severe hypophosphatemic rickets phenotype and recessive inheritance
Hereditary hypophosphatemic rickets with hypercalciuria (HHRH) is a rare disorder of autosomal recessive inheritance that was first described in a large consanguineous Bedouin kindred
Genetic studies of these disorders have identified mutations in PHEX and FGF23 as the causes of X-linked dominant disorder and autosomal dominant forms, respectively.The objective of the study was to describe the molecular genetic findings in a family affected by hypophosphatemic rickets with presumed autosomal dominant inheritance.We studied a family in which the father and the elder of his two daughters, but not the second daughter, were affected by hypophosphatemic rickets
Hereditary hypophosphatemic rickets with hypercalciuria is another rare disorder of autosomal recessive inheritance
First, we examined a kindred with a severe hypophosphatemic rickets phenotype and recessive inheritance.
Autosomal recessive form of hypophosphatemic rickets was mapped to chromosome 4q21 and identified homozygous mutations in dentin matrix protein 1 (DMP1) gene, which encodes a non-collagenous bone matrix protein.
In addition, such CLCN5 mutations that would result in a functional loss have also been demonstrated in Japanese children with idiopathic low molecular weight proteinuria, hypercalciuria and nephrocalcinosis, and an Italian kindred with X-linked recessive hypophosphatemic rickets (XLRH) and hypercalciuria.
Inactivating mutations of phosphate-regulating gene with homologies to endopeptidases on the X chromosome, dentin matrix acidic phosphoprotein 1, and ectonucleotide pyrophosphatase/phosphodiesterase 1 are associated with X-linked hypophosphatemic rickets, autosomal recessive hypophosphatemic rickets 1, and autosomal recessive hypophosphatemic rickets 2, respectively.
The objective of the study was to describe the molecular genetic findings in a family affected by hypophosphatemic rickets with presumed autosomal dominant inheritance.
The HHRH is transmitted by autosomal recessive inheritance and is an extremely rare form of hypophosphatemic rickets.
X-linked familial hypophosphatemic rickets (X.L.F.H.R.) is one of the D resistant rickets.
Iron deficiency may affect autosomal dominant hypophosphatemic rickets phenotype by regulating FGF23 production.Current treatment with activated vitamin D metabolites and oral inorganic phosphate salts may partially correct skeletal lesions and linear growth in patients with hypophosphatemic rickets.
[X-linked familial hypophosphatemic rickets report of six cases (author's transl)].

Answer: Hypophosphatemic rickets are transmitted with:
1) autosomal recessive
2) autosomal dominant
3) X-linked recessive and
4) X-linked dominant inheritance.
Exact answer: autosomal recessive, autosomal dominant, X-linked recessive, X-linked dominant